: 'Example 7-37. A random variable X assumes the value 1, 12, ... with probabilitiesU1, Uz ... respectively. Show that1u; e» (^;)* ; ^; > 0, Du; = 1j=0Pkk!=D0 is a probability distribution. Find its generating function and prove that its mean equals E (X)and variance equals V(X) + E(X).

Answered: Image /qna-images/answer/71d6466a-ff41-447b-a1d9-0e04a9b8a6df.jpg

Answered: 'Example 7-37. A random variable X…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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12
An experiment can result in one of five equally likely simple events, E₁, E₂, A: E₂, E4 2' P(A) = = 0.4 B: E₁, E3, E4, E5 P(B) = 0.8 C: E₂, E3 Refer to the following probabilities. P(A n B) = 0.2 P(AIB) = 0.25 P(BIA) P(BU C) = 1 P(BIC) 0.5 P(CIB) 0.25 Use the Addition and Multiplication Rules to find the following probabilities. (a) P(AUB) (b) P(An B) = 0.5 P(A U B) = ---Select--- + ---Select--- ✓ P(A n B) = ---Select--- (c) P(B n C) Yes P(B n C) = ---Select--- No P(C) = 0.4 . P(B) = = P(C) = = ---Select--- V = Do the results agree with those obtained by listing the simple events in each? P(A U B) = P({E₁, E₂, E3, E4, E5}) = 1 P(A n B) = P({E₁}) = 0.2 P(B n C) = P({E3}) = 0.2 .., E5. Events A, B, and C are defined as follows.
23. *An insurance policy pays an individual 100 per day for up to 3 days of hospitalization and 25 per day for each day of hospitalization thereafter. The number of days of hospitalization, X, is a discrete random variable with probability function Pr(X = k) = (1/15)(6 – k), k = 1, 2, 3, 4, 5. Calculate the expected payment for hospitalization under this policy. (213.3)
6
4.2 The probability distribution of the discrete random variable X is f(x) = 3 (*)*** Find the mean of X. 3-x (¹)ª (²³)³—ª, x = 0, 1, 2, 3.
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.
Question 5 Find the 82 -th percentile for a uniform random variable U with the lower limit 17 and the upper limit 21. The 82 -th percentile for U is (Round the answer to 2 decimal places)

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'Example 7-37. A random variable X assumes the value M, 2, ... with probabilities U1, Uz, ... respectively. Show that E u;e(^,)*; ^; > 0, Eu; = 1 Pk = k!