Answered: Suppose X is a random variable with PMF…

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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Suppose X is a random variable with E(X) = 0 and Var(X) = 2. What is E(X2 )? a). 1 b). 2 c). 3 d). 4 e). none of above
Consider a random variable X taking the values k1, k2, , km E R .. with probability ; Pn E [0, 1] 1. Write down the formula for the P1, P2, .. respectively, where p1 + P2 + expected value of f(X) for a given function f(-). + Pn ...
Let (X,Y) be a discrete random variables with joint pmf given by 1 Px,y(0,0) 4 = 1 Px,(0,1) = 4 1 Px,y(1,1)== 2 Then P(Y=1) = Select one: а. 1 3 b. 3 4 C. 1 d. 1 4
Q7. Let X; (i = 1,.,n) be a random sample from the N(u, o²) population with unknown parameters u and o?. Then we know that T, = E-1(X - X)²/(n – 1) is an unbiased estimator -xi-1 . Now consider two other estimators T, and T3 for o? where of a? and further, (n-1)T T2 = E(X – X)*/n and T3 = E(X – X)²/n + 1). %3D What is the variance of T,? Find out the variances and biases of T2 and T3 and thus obtain their m.s.e.'s. Show that among the three estimators T,, T2 and T3 the one with minimum m.s.e. is T3.
H.W:-Let x be a discreat random variable whose p.m.f If E(x)= 0.5 -1 2 P(x=x) 0.3 a Find the: 1. value a, b? 2. var (3x+3) 0.5 = -a + 2b -a + 2b =1 %3D ash.
3. Let X Geometric(p) with pe (0, 1). Prove that for every a, beN we have P(X = a+ b|X > a) = P(X = b). 4. Let X be a discrete random variable with the following distribution: P(X = -3) = a, P(X = -2) = ; P(X = 0) = 6: P(X = -1) = b, %3| P(X = 1) = c, P(X = 2) = 32 a. Find a, b, c. b. Calculate E(3+ 2X), E(3+2x)², Var(3+ 2X). 5. Derive the expected value of the random variable X with distribution Negative Binomial(r, p).
Q 6.1. Suppose Z = (Z₁, Z2, Z3) is a standard multi-variate Gaussian random variable i.e., for i ≤ 3, Zi~ N(0, 1) are i.i.d. random variables. Each of the random variables, (a)–(d), on the left is equal in distribution to exactly one random variables, (1)–(4), on the right. Pair up according to "equal in distribution" and explain briefly your reasoning. X₁ (a) X₂ (b) (x₂) - (2) (c) (x²) - (¹/1² 1/√²) (2₁) (3/√2 = √2 = (V2) Z₁ (d) (x) - (1) (²) X2 Y₁ (9)-(-) (2) (1=1) Y₂ (1) Y₁ (²) (4) - (1/² (3) (1/√√2 1/√2-1/√2) (x₁) = (²₁ ² ✓/³²) (3) 2 2 √2 1 Z3 Y₁ → ()-()) (4) = Y₂ 1/2) (2) 1) (2)
If a random variable X is defined such that E[(X -3)21 = 18 and E(X- 1)1=34, Then the values of u and a are. =3/5 and o=6 and a
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

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Suppose X is a random variable with PMF given by the following table: x = 1, 2, 3, 4