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.
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?
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 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).
Let X be a geometric random variable with p= 1/3. Compute E(X³).
Q.7) Suppose X is a random variable with probability mass function given in Question 5 (**see below) a.) Find E(X4| -1< or equal to X < or equal to 1) **Here's Question #5 Suppose X is a random variable with probability mass function given in the following table: x = -2.0, -1.0, 0.0, 1.0, 2.0 p(x) = 0.4, 0.21, 0.0, 0.13, 0.26
3. Let Y be the number of speeding tickets a YSU student got last year. Suppose Y has probabilitymass function (PMF)y 0 1 2 3fY (y) 0.12 0.13 0.33 0.42(a) What is the probability a YSU student got exactly one ticket?(b) What is the probability a YSU student got at least one ticket?(c) Compute µY , the mean of Y .(d) Find the variance and standard deviation of Y .(e) What is the probability that Y exceeds its mean value?
5
5.1 A random variable X that assumes the values X1, 2,..., xk is called a discrete uniform random vari- able if its probability mass function is f(x) = for all of 1, 2,..., xk and 0 otherwise. Find the mean and variance of X.
The random variable x is N(10,1). Find f(x(x-10)²<4).
Page 327, 5.1.7

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