Suppose that X has the discrete uniform distribution on the integers0,1,2 (i.e. P(X = k) = 1/3, k = 0, 1, 2) and that Y has a binomialdistribution with n =2 and p = 1/2. If X and Y are independent, find%3DP(X = Y).1/61/21/91/31/12

P(X=0) = P(X=1) = P(X=2) = 1/3 = 0.333 Y is binomial random variable n = 2 p = 0.5 Y = 0 P(0) =…

Answered: Suppose that X has the discrete uniform…

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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4.22 The random variable x has the discrete probability distribu- tion shown here: -2 1 2 -1 .15 p(x) .10 .40 .30 .05 a. Find P(x -1). c. Find P(-1 < x < 1). d. Find P(x < 2). e. Find P(-1 < x < 2). f. Find P(x < 1).
Suppose X has a binomial distribution with p = 0.3 and n = 10. Compute P(X=0), P(X=2), E(X) and VarX.
(5.) IF X 5. If X, Y are i.i.d N(0,0²) Y . We found out in the class that √X² + Y2 is Rayleigh distributed. Find its expectation and variance. ( • Find the cdf/pdf of the power signal X2 + Y2. What is the name of this distribution? . Find the expectation and variance the above.
A.2) The time between successive customers coming to the market is assumed to have Exponential distribution with parameter lambda. a) If X1, X2. ..., Xp are the times, in minutes, between Successive customers selected randomly, estimate the parameter of the distribution. b) The randomly selected 15 times between successive customers are found as 1.8, 1.2, 0.8, 1.4, 1.2, 0.9, 0.6, 1.2, 1.2, 0.8, 1.5, 1.8, 0.9, 1.5 and 0.6 mins. Estimate the mean time between successive customers, and write down the distribution function. c) In order to estimate the distribution parameter with 0.4 error and 4% risk, find the minimum sample size.
3: Find the theoretical frequencies, by using a suitable distribution X 0 1 2 3 4P(X) 21 / 462 140 / 462 210 / 462 84 / 462 7 / 462
The annual rainfall (in inches) in a certain region is normally distributed with µ = 40 and σ = 4. What is the probability that starting with this year, it will take more than 10 years before a year occurs having a rainfall of more than 50 inches? Suppose the rainfall in each year is independent of the rainfall in other years and the distribution of rainfall in each year is the same as in the present year.
Suppose X1, X2, ... , Xn is a random sample and Xi = {1, with probability p 0, with probability 1-p} for every i = 1, 2, ... , n. Find the Moment Generating Function of ∑i=1n Xi . What is the distribution of ∑i=1n Xi ?
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.
2.Suppose that the return R (in dollars per share) of a stock has the uniform distribution on the interval [-3,7]. Suppose also, that each share of the stock costs $1.50. Let Y be the net return (total return minus cost) on an investment of 10 shares of the stocks. Compute E(Y).
The profits of a mobile company are normally distributed with Mean of R.O (17x 10) and standarddeviation of R.O (17).a. Find the probability that a randomly selected mobile has a profit greater than R.O ((17x10) +10)
Suppose that we have 3 random variables, W, X and Y, defined as follows: - W follows a t-distribution with 7 degrees of Freedom. - X follows a chi-Square distribution with 10 degrees of Freedom. - Y follows a f-distribution with 2 and 5 degrees of Freedom.1.1. P(W<1)1.2. P(-1<W<0.5)1.3. P(X<10)1.4. P(X>5)1.5. P(4<X<9)1.6. P(Y<1.5)1.7. P(Y>0.2)
) Let Yhave a binomial distribution with parameters n and p. H,: p= 1 is rejected 1 is accepted if Y2 c. Find n and c to give a power function T(p) 2 and H,:p> so that a = 0.10 and T = 0.95 , approximately.

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Suppose that X has the discrete uniform distribution on the integers 0,1,2 (i.e. P(X = k) = 1/3, k = 0, 1, 2) and that Y has a binomial distribution with n = 2 and p = 1/2. If X and Y are independent, find P(X = Y ). 1/6 O 1/2 O 1/9 1/3 1/12