Problem #5: An assembly consists of two independent mechanical components. Suppose that the probabilities that the firstand second components meet specifications are 0.97 and 0.83, respectively. Let X be the number of componentsin the assembly that meet specifications.Problem #5(a):Problem #5(b):(a) Find the mean of X.(b) Find the variance of X.Round your answer to 4 decimals.Round your answer to 4 decimals. Problem #4: Suppose that the probability mass function for a discrete random variable X is given byp(x) = cx, x = 1, 2, ..., 8.Find the value of the cdf F(x) for 5 ≤ x ≤ 6.(You will need to find the value of c so that p is a probability mass function.)Problem #4:

As per the Bartleby guildlines we have to solve first question and rest can be reposted... 4...…

Answered: Problem #4: Suppose that the…

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...

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3. Suppose that X is a discrete random variable with probability mass function (pmf) as summarized in the table below. -3 f(x) 0.35 0.25 0.4 Find the cumulative distribution function (cdf) F(x) of X. You may either write F (x) as a piecewise defined function or sketch a graph of F(x). Also, no work is required to be shown in this problem.
1. Let X be a Poisson random variable on the non-negative integers with rate λ = 4. Let W = 2X + 10. (a) What is the range of W? (b) Find a formula for Pw(k).
Q.7) Suppose X is a random variable with probability mass function given in Question 5 (**see below) a.) Find E(X4| -1< or equal to X < or equal to 1) **Here's Question #5 Suppose X is a random variable with probability mass function given in the following table: x = -2.0, -1.0, 0.0, 1.0, 2.0 p(x) = 0.4, 0.21, 0.0, 0.13, 0.26
2. A random variable X has a probability mass function given by: 1 0.2 a. Determine P(x) = 2 b.Find P(X<2) c. Find P(X≥ 3) X P(x) 0 0.1 2 ? 3 0.4
3. Suppose X is a discrete random variable with pmf defined as p(x) = log10 ( for %3D x = {1,2,3,...9} Prove that p(x) is a legitimate pmf.
3. Suppose it is known from large amounts of historical data that X, the number of cars that arrive at a specific intersection during a 20-second time period, is characterized by the following discrete probability function: 6x f(x) = e-6, for x = 0,1,2, ... a) Find the probability that in a specific 20-second time period, more than 8 cars arrive at the intersection.
Suppose that X1, X2, ..., Xn is a random sample with a probability law P(x) = {0x, 0 Where 8 is an unknown parameter. si x = 1,2,3, 4; otherwise A. Get an estimator of 0 by the method of the moments. B. Prove that the estimator is unbiased.
QUESTION 4 The probability density function for the time taken to complete a 1-hour test (X) by students is given by a) b) c) Find the value of c. f(x) = {cx² + x ! ) 0≤x≤1 elsewhere Find the probability that a randomly selected student will finish in at least half an hour. Calculate the variance of X.

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Problem #4: Suppose that the probability mass function for a discrete random variable X is given by p(x) = cx, x = 1, 2, ..., 8. Find the value of the cdf F(x) for 5 ≤ x ≤ 6. (You will need to find the value of c so that p is a probability mass function.) Problem #4: