(1) Let X be a random variable with a function (3 4 x! (3-x)! S(x) =- x= 0,1, 2,3 . then E(x+1)is o.w (d) , (e) None of these 7/2

Q: (37) Let X be a random variable with p.d.f. (x+1)e2* x=1,2,3 f(x) =- , find (1) k (2) E(x² +1) O.w

A: The probability distribution table is obtained as :  x 1 2 3 f(x) 2e2k 3e2k 42k Every…

Q: Independence). (i) Recall that given events A, B,C, we have that P(AUBUC) = P(A)+ P(B)+ P(C) – P(An…

A: Hello! As you have posted 3 different questions, we are answering the first question. In case you…

Q: A random variable X is defined by X =- 2 = 3 with a prob. of 113 with a prob. of 1/2 with a prob. of…

A: Given, X -2 3 1 P(X) 1/3 1/2 1/6

Q: 1 The discrete random variable X has Var (X) = 5 Find Var (4X – 3)

A: Given Data: Var(X)=5 Equation: Var(4X-3) ......(1) Simplify the equation (1). Var4X-3=42VarX=16VarX

Q: Find (a) The constant K (b) P(X> 1) (c) P(|x|<3)

A: To determine the value of K we will use the fact that the integration of pdf f(x) over whole range…

Q: 4. (a) Consider a nonnegative, integer valued random variable Y, and a random sample X1, ·.. , Xn.…

A: Expectation gives the most likely value of a random variable.

Q: (45) Let X be a random variable with p.d.f. ((k + 4)(x+2) 0<x<2 f(x)=- find (1) k (2) E(x) O.W

A: (45) (1) The random variable X with p.d.f is, fx=k+4x+2      0&lt;x&lt;20…

Q: (7) Suppose that X₁ and X₂ are two random variables with j.m.g. f. 2 (t₁ - 1)(t₂-1) + (t₂ − 1)² '…

A: It is given that the two random variables X1 and X2 has the m.g.f as below: MX1,…

Q: (34) Let X be a random variable with p.d.f. 1<x<» k f(x) = { find k. O.w

A: Formula used: fx=x-2k           1&lt;x&lt;∞0                   Otherwise

Q: 5) Let N= [0, 1) and let F = o ([0, 1/3), [1/3, 2/3), [2/3, 1)) (a) Write down F. (b) Is X(w) = 2w…

A: Given, Ω=0,1→Sample spaceF=σ0,13,13,23,23,1→sigma field

Q: ) Let X be a random variable with p.d.f. 2k x = 1,2,3 (х - 1)! f (x) = find (1) k (2) E(2x) O.W

A:

Q: Let X be a random variable with p.d.f. [(k +4)x 1<x<5 f(x) = , find (1) k (2) Var(x) O.W

A: Let X be a random variable with p.d.f. fx=k+4x      1&lt;x&lt;50                  otherwise   1) We…

Q: Let X be a random variable with p.d.f. 4k 1< x<10 f (x) =< find k. O.W

A:

Q: If E and F are two independent events, such that P (E ∩ F ) = 1/6 , P (E' ∩ F' ) = 1/3 and (P (E) −…

A:

Q: We know that X is an unknown distribution with a mean of u and a variance Xị are i.i.d. e

A: From the given information, X is an unknown distribution with a mean of μ and a variance of σ2; And…

Q: (1) Let X be a random variable with a function [A(3x² +6) -1,0,1,2 . then (0) k = (6) k = (e) * (d)…

A:

Q: 1. Let (X) be a simple random walk that starts from X, = 0 and on each step goes up one with…

A: Hello thankyou for the question As per the honor code, we are allowed to answer three parts at a…

Q: 3. Let the random variable X have the pmf f(x) = = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² for x =…

A: The provided information is as follows:The probability mass function of  is .

Q: 7. If X is a random variable with fx Let Y = 3√In X. (a) Fx(x) ) = 1, 1<x<e (b) Fy(y) (c) fy(y)

A:

Q: Suppose X and Y are two independent and identically distributed geometric random rariables. The pmd…

A: PMF of X is given by, P(X=x) = p(1-p)x-1 , x=1,2,3.... Now,  ⇒P(X≥x)= ∑t=x∞ P(X=t)= ∑t=x∞p(1-p)t-1 =…

Q: Suppose that X, and X2 are aiscrete random variables with joint pdf of the form f(x1,x2) = c(x1 +…

A:

Q: Let M and N be two independent events such that P(M) = 1/3 and P(N) = 1/4. Find P(M/N')

A:

Q: Let probability that a child will be born with black eyes is 1/3, determine the probability that…

A: It is given the probability that a child will be born with black eyes is 1/3 i.e. p=1/3. It has been…

Q: 4. Let X be a random variable taking positive values and assume that E(X) exists. Which of the…

A: Option (I) is correct as E(X2)&gt;= (E(X))2 when we find Variance.

Q: (a) Discuss the two expressions 2(x₁ - x)² and (-1) 2(x,-)², both of which are used to measure the…

A: Solution: As per the guidelines only first three sub parts should be answered. In case the remaining…

Q: (3) Let X be a random variable with p.d.f -(3x+6) 15 0<x<1 f(x) =- then E(Gx) is O.w 4 7 15 (b) 15…

A: We want to find correct answer for question

Q: 1-4x 10) If a random variable assumes 4 values with probability 1+3x 1-x 1+2x and ¹-4 4 4 4 the…

A: Here for given probability check whether using value of x total probability is equal to 1 and all…

Q: 1+3x 1-4x (10) If a random variable assumes 4 values with probability 1+1 1+2 and the condition on x…

A: A random variable assumes 4 values with probability p1=1+3x4 , p2=1-x4 , p3=1+2x4 , p4=1-4x4

Q: (1) Let X be a random variable with a function x= 0,1, 2,3 4 xt(3-x)! S(x)=- , then E(x+1) is o.w…

A:

Q: (b) Let X~N(40,144) and if Y = 2X - 1 Find the following probabilities: (i) P(X 50) (iii)P(35 < X S…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: (33) Let X be a random variable with p.d.f. e2k x= 1,2,3 f(x)=- find (1) k (2) E(x+1) O.W

A: Given that X is a random variable with p.d.f f(x)=e2k ; x=1,2,30     ; Otherwise.

Q: (13) Let X be a random variable with p.d.f. 2e-2x 0<x<0 f(x) ={ , find E(e2*) O.W

A: Solution :  Given :  f(x) = 2e-2x    0&lt;x&lt;∞0   o.w     E( e-2x )  = ∫x e-2xf(x) dx…

Q: 2) Let X₁, X₂, X3, X4 be a random sample of size 4 from a population with the following distribution…

A:

Q: (1) Let X be a random variable with a function [3 1 x= 0,1,2,3 4 x! (3-x)! fx) = { , then E(x) is…

A: Given, X is a random variable with the function below

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!