3.2. The probability mass function of the random variable X is given as follows.X-369p(x) = Pr(X=x)1/61/21/3a) Compute the values of E(X) and E(X²).b) Compute the value of E{(2x+1)²} by using the theorems related to the expected value.3.3. The probability mass function of the discrete random variable X is given as follows.-2124p(x) = Pr(X=x)1/41/81/21/8Plot the cumulative distribution function, Fx(x) of the random variable, X.

1) a) E(X) is given as, E(X)=∑x∗P(X=x)=−3∗1/6+6∗1/2+9∗1/3=5.5 E(X^2) is given as,…

Answered: 3.2. The probability mass function of…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
Q.1 The probability mass function for a discrete random variable X is defined as ((1+0)" (^) 0x; x = 0, 1, 2, 3, ..., n fx(x) = {(1 + 0; e. w. where > 0. Show that it is probability mass function. Find its mean and variance.
Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is the expected value of the random variable X and varX = E(X - μ)^2 is the variance of the random variable X. Guidance: start from the representation - (X-a)^2 = (X µ + μ- a)^2 and group the right side of the representation appropriately into the form (Z + b)^2, where Z is some random variable and b is a real number and open the square. The task should be solved with the help of the expected value calculation rules.
1.4 Let X be a continuous random variable with pdf, fx(x), and fx(t+5) = fx(5 – t) for all t> 0. Please provide the mean of X.
Suppose X and Y are two random variables with E[X] = 1, Var (X) = 4, E[Y ] = -1, Var (Y) 4, and Cov (X, Y) = 1. Find the standard deviation of (X - Y). = (a) 2 (b) √2 (c) 6 (d) √6 (e) None of the above
(ii) Suppose that X₁ and X₂ have joint pdf 2, 10, Compute the joint pdf of random variables Y₁ = X₁ and Y₂ = X2. f(x1, x₂): for 0 < x1 < x₂ < 1 otherwise =
3. Let the random variable X have the pmf f(x) = a) E(X) b) E(X²) c) E(3X²2X + 4) (x+1)² 9 for x = -1,0,1. Compute
9. If X and Y are two random variables and let g(X) be a random variable. Show that (a) E[g(X) X=x] = g(x). (b) E[g(x)Y|X=x] = g(x) E[Y|X=x]. Assume that E[g(x)] and E[Y] exist.
Find the value of P(X 3) if X is the discrete random variable taking values X1, X2, X3 where P(X= 0) = 0, P(X-D1) = 1/6 and P(X = 2) = 4. a. 1 b. 1/12 c. 7/12 d. 1/4
4b)
Fact: If X is a compound random variable with X = ₁X₁, then E(X) = E(X₂) E(N) i=1 a. when X₁ are all discrete b. when X₁ are all continuous
Suppose that a random variable X is an Exponential Random Variable with parameter β = 3.(a) What is E(X)?(b) Compute P(X > 2).(c) Compute P(X > 5 |X > 3).

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