5. Suppose that X is a discrete random variable with probability density functionх%3D1, 2, 3, 4.p(x) = cx²,(b) Find E(X) .Select one:O a. noneO b. 6.7О с. 3.3O d. 5.2

In question, We have given the pdf of X which is f(x). Then we'll find the value of E(X). The…

Answered: 5. Suppose that X is a discrete random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

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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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5. Suppose that X is a discrete random variable with probability density function x = 1, 2, 3, 4. p(x) = cx², (a) Find the value of c. Select one: О а. 1/25 O b. 1/30 О с. 30 O d. none
10. Let X be a continuous random variable that only takes on non-negative values. Suppose E(X)=4 and V(X) = 1, which of the following statements are necessarily true? O Pr(2 { Pr(X > 8) { 3 4 O Pr(X > 10) < 16
. Determine the value for c and the covariance and correlation for the joint probability mass function fXY (x, y ) = c (x + y) for x = 75, 75+1, 75+2 and y = 75, 75+1, 75+2. (Round up after multiplying) (Sum of probabilities = ?)
9. Consider the formula: P(x) = x/21, x 0, 1, 2, 4. Is P(x) a probability mass function? If so, show the distribution of X in tabular form and compute the expected value of X.
1) Suppose that Y₁, Y2,...,Y₁ is a random sample from a population with probability density function 1,7, f(x)=B³ Find the Maximum Likelihood Estimator of B. 00 elsewhere
b) The continuous random variable Y has the following probability density function. Pembolehubah rawak selanjar Y mempunyai fungsi ketumpatan kebarangkalian seperti berikut. Jh(3y² +2) ; -2sys2 0 ; otherwise f(y)={ 1 Show that h=- 24 i. 1 Tunjukkan bahawa h=; 24 ii. Based on the value in part (i), find the cumulative distribution function F(y). Berdasarkan nilai dalam bahagian (i), cari fungsi taburan longgokan F(y).
2. a. If X is a discrete random variable with probability mass function P(X =x) and a, b are constants, prove that E(aX +b)= aE(X)+b, ii. Var (ax +b)=a³Var(X). i.
9. Given that f(x, y) = (2x+2y)/2k if x = 0,1 and y = 1,4, is a joint probability distribution function for the random variables X and Y. Find: (f(x|y = 1)
2. Suppose that X and Y are independent random variables, both with the standard normal distribution i.e. X, Y~ N(0, 1). For pe [-1, 1], define Z:=√1-p²X + pY. Show that E[Z|Y] =pY.
3. Suppose X and Y have joint probability density function f(x, y) = {* S6x, 0 < x< 1,0 < y <1- x elsewhere. Determine whether the two random variables are dependent or independent. b. If the value of Y is 0.5, what is the probability that X will have a value greater than 0.3? а.

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5. Suppose that X is a discrete random variable with probability density function х%3D1, 2, 3, 4. p(x) = cx², (b) Find E(X) . Select one: O a. none O b. 6.7 О с. 3.3 O d. 5.2