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.
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10. Let and be independent random variables representing the lifetime (in 100 hours) of Type A and Type B light bulbs, respectively. Both variables have exponential distributions, and the mean of X is 2 and the mean of Y is 3. a) Find the joint pdf f(x, y) of X and Y. b) Find the conditional pdf f₂ (ylx) of Y.. c) Find the probability that a Type A bulb lasts at least 300 hours and a Type B bulb lasts at least 400 hours. d) Given that a Type B bulb fails at 300 hours, find the probability that a Type A bulb lasts longer than 300 hours. e) What is the expected total lifetime of two Type A bulbs and one Type B bulb?
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.
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Let X be a random variable taking positive values and assume that E(X) exists. Which of the following statements are true? • (i) E(X*) > (E(X))*. • (ii) E(1/X²) > 1/E(X²). • (ii) E(e-3X) > e°
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