Problem #4: Let X be a continuous random variable with probability density functionS2x20Problem #4:f(x) =Let U = 2-x > 2otherwiseforfor X 2. Find P{U > 31.Enter your answer symbolically,as in these examples

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Answered: Problem #4: Let X be a continuous…

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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4. The cumulative distribution function of a continuous random variable, X is given as follows: x<0 F(x) = - x(x+4), 32 0Sx<4 1 x24 (a) Calculate P(|X-1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).
4. Sixteen-ounce boxes of shredded wheat cereal packed automatically by machine are sometimes over- weight and sometimes underweight. The actual weight in ounces over or under 16 is a random variable X whose probability density is f(x) = c(4- x²) for -2 < x < 2, and 0 elsewhere. Negative values pertain to ounces under 16. Determine the constant c, and then find the probability that a box of cereal will be (a) more than one ounce underweight.
Please answer both parts of the question clearly thanks
An individual has a vNM utility function over money of u(x) = Vx, where x is final wealth. Assume the individual currently has $16. He is offered a lottery with three possible outcomes; he could gain an extra $9, lose $7, or not lose or gain anything. There is a 15% probability that he will win the extra $9. What probability, p, of losing $7 would make the individual indifferent between to play and to not play the lottery? (Make sure to answer in the form, 0.X, i.e. 0.25) Enter your answer here
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1. The probability density function of a random variable X is given by f (x) : 1 ex/300 300 for x 2 0 and f (x) = 0 for x < 0. Find P (X s 600).
Example 2.1.1 Let S = R, and suppose P is a probability measure on R. Define F(x) by F(x) = P((-∞, x]), XER. (2.3) Then (i) F is right continuous,
Example 2.19 Let X be a random variable with possible values {x1, x2,...x) such that P(X = x) =!v i. Find E(X).
Question 2.1 The joint probability function of X and Y is given by f(x, y) = (1/20) * (x + 3y)for 1 < x < 3 and 0 < y < 2. Find; a. P (0 < x < 2)
g(x) = 3 4+1 if n < x < n + 1 given this function for all nonnegative integers n=0,1,2,3,... and g(x)=0 otherwise. (Hint: I strongly suggest that you graph this function.) 1. Can px(n)=g(n) be the probability mass function of a discrete random variable X that takes values in Z? If not, why, and if so, solve the E[X] and Var(X). 2. Can pY(y)=g(y) be the probability density function of a continuous random variable Y? If not, explain why, and if so, compute E[Y] and Var(Y).

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Problem #4: Let X be a continuous random variable with probability density function S2x2 0 Problem #4: f(x) = Let U = 2- x > 2 otherwise for for X> 2. Find P{U>1). Enter your answer symbolically, as in these examples