b) Two PINS are chosen independently and at random, and you are given that each consists of four different digits. Let X be the random variable denoting the number of digits that the two PINS have in common. i. Explain clearly why P(X = k) = ,for k (0, 1, 2, 3, 4. () ii. Hence write down the values of the probability mass function of X, and find its mean.

b) Two PINS are chosen independently and at random, and you are given that each consists of four different digits. Let X be the random variable denoting the number of digits that the two PINS have in common. i. Explain clearly why P(X = k) = ,for k (0, 1, 2, 3, 4. () ii. Hence write down the values of the probability mass function of X, and find its mean.

Name: b) Two PINS are chosen independently and at random, and you are given
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: b) Two PINS are chosen independently and at random, and you are given that each PIN consistsof four different digits. Let X be the random variable denoting the number of digits that the twoPINS have in common.i. Explain clearly why P(X = k) =-for k

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Related questions

Q: A. Let X1, ... ,X10 be N(0,0) and, Let a = 0.05, and B = 0.10. We wish to test Ho:0 = 4 versus HA: 0…

A: Sequential Probability Ratio Test The best known procedure in sequential testing is the Sequential…

Q: Four buses carrying a total of 160 students from the same school arrive at a football stadium. The…

A: Given that Total students =160 Number of buses=4 Let X denotes the number of students that were on…

Q: If the probability density function of the random variable X is x>0, f(x)= 0, Otherwise. Then the…

A: Given data : f(x)=e-x , x>0 0 , otherwise Finding Mean ,…

Q: Find the expected value of q. d. Let X1, X2,., Xn be i.i.d. Bernoulli(p). Suppose q =

A: Bernoulli Trail: In probability theory, a Bernoulli trial is a random experiment which has exactly…

Q: Q 51. Coin Game: You and your two friends play the following coin game: You each flip a fair dime…

A: a) Sample Space, S = {sijk} = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} where, i = my outcome j = 2nd…

Q: If a random variable X is defined such that: E[(X - 3)2] = 18 and E[(X – 1)²] = 34. Then the values…

Q: Consider random variables X and Y with x = 0 x = 1 fx,y(x, y) in the table. Find fxy (1|0) and…

A: Let X and Y be represent the random variable having joint probability distribution f(x,y) We have…

Q: You have two fair coins. The first coin is tossed five times. Let the random variable X be the…

A: Let X be the number of heads when we toss the coin five times. Then X represent a Binomial…

Q: I are independent. Eunction of W given L = 2. a formed A = Lx W Find the range

A: *Answer: Since there are multiple questions, according to Bartleby policy we will answer the first 3…

Q: I. Let X be the number of courses that thirty part-time students were taking this term. The…

Q: The joint probability mass function of the random variables (X, Y) is given by the followin cable.…

A: We have given joint distribution of X and Y and we have to find the var(X+Y)

Q: The common probability function of X and Y random variables like this a. Find the value of Cov (X,…

Q: The probability generating function for a random variable X is given by: gx(2) ==z? +10+z20+25 (2)X6…

A: From a given probability generating function of X, we need to find required conditional probability.

Q: Let X and Y be dependent random variables. Which statements are always true? Select one or more:…

A: # Let X and Y be dependent random variables. Which statements are always true?

Q: Q5. A box of 10 transistors is known to contain 2 that are defective. The transistors are to be…

A: A box contain 10 transistors is known to contain 2 that are defective.N (sample size)=10d(no.of…

Q: Let X be a regular random variable, then V( E(X)) = OA. V(X). O B. some positive number. OC. EX).…

A: Random variables are of 2 types, discrete and continuous. A discrete random variable can only take…

Q: 3. Find the probability mass function of the random variable Y which represents the number of red…

A: Introduction: The random variable Y is the number of red marbles when 3 marbles are drawn at random…

Q: Suppose the probability that Jimmy gets a hit on a given at-bat is 1⁄4. Let X denote the number of…

A: In this case, each of the at-bats has the only option of being "a hit" (defined as success) or "not…

Q: Let Xn Exp(4), n > 1, be independent random variables. Estimate the probability that 1 S100 2

Q: The probability mass function of a random variable X is as follows: frx) = x! x = 0, 1, 2, ... Given…

Q: Let X and Y be discrete random variables with joint probability function: P( x, y ) = ( 2x + y )/12,…

A: Let X and Y be discrete random variables with joint probability function:P( x, y ) = ( 2x + y )/12,…

Q: Suppose X is a random variable and suppose the possible values that it can assume are given by a, b,…

A: Given, X is a random variable

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.2, an

A: Given information: Var(X)=1.6 Var(Y)=1.2 Cov(X,Y)=0.6 Let Z = -1.2X + 1.9Y + 4.2.

Q: Find the variance of probability function 1 2 4 P(X) 0,25 0,15 0,10 0,25 0,25 21 - O A) 6,80 O B)…

A: Here, X P(X) X.P(X) X2 X2.P(X) 0 0.25 0 0 0 1 0.15 0.15 1 0.15 2 0.1 0.2 4 0.4 3 0.25…

Q: What is the probability of the event {X = 1}? 2. Write the event {X = 2} in terms of the events {D1…

A: As per policy I have calculated 3 subparts kindly REPOST for remaining parts. You roll a fair…

Q: Let X and Y be two independent random variables such that E[X]=3, E(Y)=4, V(X)=10 and V(Y)-20. Then…

A: According to the given information, we have E(X)=3E(Y)=4V(X)=10V(Y)=20

Q: b) The probability density function of random variable X is given as: if 0<x<1 otherwise (A– Bx the…

Q: Q4. The following table shows the probability mass function for the discrete random variable X: k 2…

Q: Contracts for two construction jobs are randomly assigned to one of or more of three firms, A, B,…

Q: b) Two PINS are chosen independently and at random, and you are given that each PIN consists of four…

A: Let X be a random variable such that X: Number of digits that the two pins have in common Now, The…

Q: Let X and Y be random variables. Suppose Var(X) = 1.6, Var(Y) = 1.5, and Cov(X, Y) = 0.1. Let Z =…

A: Solution: From the given information, Var(X) =1.6, Var(Y) =1.5 and Cov (X, Y) =0.1. Let Z =…

Q: box A and box B both contain the numbers 1 2 3 and 4. Construct the probability mass function and…

A: Given, Box A 1 , 2, 3 , 4 Box B 1 , 2, 3 , 4

Q: c. What is the height of this rooted tree? V6 V3 V4 v10 V12 V17 V16 V14• V15 v13 V19 V18

Q: The Denver Post reported that, on average, a large shopping center had an incident of shoplifting…

A: Given, The Denver Post reported that, on average, a large shopping center had an incident of…

Q: 5. Calculate the value of k so that the function f(x) = k/5ª. N, set a probability function of a…

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

b) Two PINS are chosen independently and at random, and you are given that each PIN consists
of four different digits. Let X be the random variable denoting the number of digits that the two
PINS have in common.
i. Explain clearly why P(X = k) =-
for k = 0, 1, 2, 3, 4.
ii. Hence write down the values of the probability mass function of X, and find its mean.

Given that a random variable X have a Poisson distribution with A;
Find E[cos(nX)] if E(X) = In 2

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Step 7

Step 8

Step 9

Step 10

Step by step

Solved in 10 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Solve c,d
What values of a, b, c, and d should be used to calculate the probability shown below? xy OSxs1 1
Answer d, c, f
A screening test for a particular infectious disease shows a positive test result in 90% of all cases when the disease is actually present, and in 10% of all cases when it is not. Assume that t% of the population is infected, where t is = 1. For a randomly chosen from the population person, find the probability that the person is actually infected if the test shows positive.
O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %D
Choose ALL THE CORRECT STATEMENTS in the following ones about probability distribution. i. Probability mass function indicates the probability distribution of a continuous random variable. ii. Probability mass function indicates the probability distribution of a discrete random variable. iii. The probability mass function of a discrete random variable X at a is denoted by P(X < a). iv. The probability function of a continuous random variable Y can be described by using P(Y= a).
Exercise 3. Let X be a random variable with mean and variance o². For a € R, consider the expectation E((X-a)²). a) Write E((X-a)²) in terms of a, u and o². b) For which value a is E((X - a)²) minimal? c) For the value a from part (b), what is E((X-a)²)?
59% Consider the joint probability function: X12 Y -1 a 0.1 0. b d 1. e 0.3 0.4 If X and Y are independent random variables the yalue of b and d are 2. A) b = 0, d = 0.2 B) b 15 d = 0.2 C) b = 15 d = 0.6 D) b = , d = 0 15 A) b = 0, d = 0.2 C)b ==,d- 0.6 15 Dowaload XFull sen ...
Solve the last part please
2. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.
In the transmission of digital information, the probability that a bit has high, moderate, and low distortion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: (c) E(X)= i Round your answer to two decimal places (e.g. 98.76).
Choose points from (0, 1) uniformly and add the numbers together. Stop this process when your add is greater than one. Let N be the random variable which is the number of points that you selected. Find E(N).