7. A discrete random variable Y has the following probability distribution.Y=yP(Y=y)11/8where k is a constant.a) Find the value of k.b) Find P(Y≤4).c) Find P(Y>3).23451/41/3k1/8

Step 1: Solution (a): We are given the probability distribution Y=y12345P(Y=y)814131k81Where k…

Answered: 7. A discrete random variable Y has the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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The discrete random variable Y has probability distribution given by: Y 0. 1 3. P(Y=y) b. 0.1 0.15 a where a, b and c are constants. P(Y = 1) = P(Y 23) %3D P(Y = 0) = P(Y = 2) – 0.1 %3D %3D Find the values of a, b and c.
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V:59)
Q6
QI: Let x be random variable with the following (p.d.f): x20 f(x) = 0. W Find: 1. The constant C? 2. The c.d.f ? 3. P(10 f(x) = O. W 1. Write the moment generating function for X ? 2. Use this moment generating function to compute the first and second moments of X ? Q3: Suppose the (p.m.f) f the random variable X is 3 f(x) 0.2 0.1 0.4 0.3 Find: 1. The V(x)? 2. The E(4x) ? 3. The E(3x+2x)? Q4: Find the V(x) by using the mgf of the random variable x that has the pmf equal to 0.5 for x=-2 and x= 2 ? Q5: If X be random variable such that E[(X - 1)1 = 10, E[(X - 2)21 = 6, find V(x)? Q6: Given that has the following (p.m.f): f(x) = ;x = 0,1, 2, 3 Find the moment-generating function of this random variable and use it to calculate V(x) ? 07: Let x be random variable with the following (p.d.f): f(x) = 0. W Such that P(x < M (0)) Compute the value of b? %3D
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7. A discrete random variable Y has the following probability distribution. Y=y P(Y=y) 1 1/8 where k is a constant. a) Find the value of k. b) Find P(Y≤4). c) Find P(Y>3). 2 3 4 5 1/4 1/3 k 1/8