Suppose for this random variable X we want to compute P(X ≤ 3) Let X be a random variable with cumulative distribution function given byx < 22 < x < 44 < x.Fx (x) =(x – 2)4/161In Figure 2.5.2, we present a graph of Fx.1.0F0.50.0134XFigure 2.5.2: Graph of the cdf Fx in Example 2.5.3.

Answered: Image /qna-images/answer/280a4cc7-f61d-40c0-9d3c-cf7f5500f6e6.jpg

Answered: Suppose for this random variable X we…

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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Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
= 3. Propose an algorithm for simulating the occurrence of two dependent events A and B that uses only one uniform random variable U~Unif(0, 1). Assume that the probabilities P(A) ΡΑ, P(B) = PB, and P(AUB) = q are given, where PA, PB, q = (0, 1) and max(PA, PB) < q < PA+PB· Formulate your answer in the form of the following statement: "if U E ..., then event A occurs; if U € .……., then event B occurs."
Show that the CDF of a geometric random variable with parameter p can be expressed as
Suppose X is a discrete random variable. Let the pmf of X be equal to 5 - x f(x) = x = 1,2,3,4 10 Find the cdf of X, that is F(X).
A red die is rolled and then a green die. Let X=2(Spots on Red) + (Spots on Green). Determine the pmf for the random variable. In particular f(6)
Suppose the CDF of a random variable x is given by x2)?
Consider a random variable, X, where X~N(17,4). Which of the following statements are true? Select all that apply. P(X > 17) = P(X 17) = P(Z > 0) P(X < 11) = P(Z < 3) P(X < 21) = P(Z < 1) P(X < 21) = P(Z < 2)
4 Suppose that Alejandro is planting a garden of tulips. Let X be the Bernoulli random variable that returns 1 if the tulip is red, and 0 otherwise. Suppose Y is another Bernoulli random variable, independent of X, that returns 1 if the tulip survives longer than 30 days, and 0 otherwise. Both X and Y have parameters 1/2. Let Z be the random variable that returns the remainder of the division of X +Y by 2. For example, if X = 1 and Y = 0, Z = remainder() = 1 (a) Prove that Z is also a Bernoulli random variable, also with parameter 1/2. (b) Prove that X, Y, Z are pairwise independent but not mutually independent. (c) By computing Var[X+Y+Z] according to the alternative formula for variance and using the variance of Bernoulli r.v.'s, verify that Var[X+Y+Z] = Var[X]+Var[Y] +Var[Z] %3D (observe that this also follows from the proposition on slide 5 of the lecture segment entitled "Binomial distribution").
Suppose X is a uniform random variable where X is from 0 to 10. What type of random variable is X? continuous and uncountably infinite discrete and finite continuous and finite discrete and uncountably infinite
4 of these 1 5 of these 3 of (a) 1.0211 (c) 1.5207 (e) 1.2962 these 2 (a) 0.1111 (c) 2.3333 (e) 12.9375 2 of these 16 tickets total 3 FIG. 5. 2 of these 26. Let X be the random variables described in Fig- ure 5. Find E(√x + 1). (b) 2.3125 (d) 0.4613 X Random draw from the box 27. Let X be the random variable described in Figure 5. Find E(X³ | X < 2). (b) 0.5625 (d) 1.3125
Example 2.8. Suppose X is a random variable whose CDF is: 3 Fx(z) = lp1.00)(2) + 100.0)(2) +20.00)(2) + Ig0,(?) Determine the following: a) fx(1) b) fx(0.1) c) fx(100) d) P(х > 105) e) P(0 0.1)
X is an poisson random variable with parameter λ = 4 Calculate P {X ≤ 3}

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