2. Let X and Y be independent random variables with E[X] = 4, Var[X] = 84, E[Y] = 6, and Var[Y] = 54.Find E[5X + 2Y - 18]- b. Find E[-3Y+X+3]-a.-с.Find E[X2]d. Find oxe. Find E[Y2]f. Find Oyg. Find Var[X+3Y - 6]h. Find Var[3X - 2Y + 35]Find E[(2X - 8)/5]j. Find Var[(2X - 8)/5]i.

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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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2. Let X be a random variable with p.m.f., (1+ x? f(x) = -,x = -1,0,1,2,3 20 0 ,otherwise. Find E(3X2 + 6).
Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)
In a random experiment if a coin is tossed three times or three coins are tossed one time, if random variable X is the number of appearances of Tails, the value of E(X), will be; Select one: O a. None O b. 3.5 O c. 2.5 O d. 1.5
Suppose X-U (-54, 60) and F(t) is the cumulative distribution function. What is the probability that X is in the interval [-51, -21] or in the interval [-36, 57]? O (F(-21)-F(-51))+ (F(57) - F(-36)) O (F(-21)-F(-51)) x (F(57) - F(-36)) O F(-21)-F(-36) O F(57) - F(-51)
2. Let the independent random variables X1 and X2 have Bin(0.1,2) and Bin(0.5, 3), respectively. (a) Find P(X1 = 2 and X2 = 2). (b) Find P(X1 + X2 = 1). (c) Find E(X1 + X2). (d) Find Var(X1 + X2).
Let X and Y denote two random variables. Which of the following can be used to compute Var(X)? A. E[Var(X|Y)] + Var(Var(X|Y)) B. E[E[X|Y]] + Var(Var(X|Y)) C. E[Var(X|Y)] + Var(E[X|Y]) D. Var(E[X|Y]) + Var(Var(X|Y))
Prob ... solve Q 1 & Q 2 please ?
The random variable x is N(10,1). Find f(x(x-10)²<4).
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%3D Let X and Y be independent random variables with E[X] = 4, Var[X] = 84, E[Y] = 6, and Var[Y] = 54. -a. Find E[5X+ 2Y - 18] - b. Find E[-3Y+X+3] Find E[X2] c.