Answered: Q.1 The probability mass function for a… | bartleby

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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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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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?
For what values of k canf(x) = (1 − k)kx serve as the values of the probability distribution of arandom variable with the countably infinite range x =0, 1, 2, ...?
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Q 4. (a) (i) Show that if U and V are independent random variables having chi-square distributions with vị and v2 degrees of freedom respectively, then X = is a random variable having an F distribution with vị and v2 degrees of freedom , i.e. a random variable whose probability density function is given by f (x) = I (4)r (4) (v½. 1+-x (ii) Using (i), or otherwise, show that if S? and S are respective variances of independent random samples of sizes nį and n2 from normal populations with variances a? and ož, then Y %3D is a random variable having an F distribution with n1 – 1 and n2 – 1 degrees of freedom. (b) Let X be a random variable modeling the heights of all adults in the population where o² is known. (i) For a random sample X1, X2, ..., Xn, state the sampling distribution of Š when n > 30. (ii) A random sample of 50 adults gives a mcan of 174.5 cm. Given that o = 6.9 construct a 98% confidence interval for µ, the mean height of all adults. Based on the confidence interval…
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13. A discrete random variable has probability function f (x) = 1/ 2* where x = 1, 2, .... Find (a) the mode, (b) the median, and (c) compare them with the mean. 14. A continuous random variable X has probability density given by x > 0 x< 0 fx (x) = {2e-2x (a) Find (i) E(X), (ii) E(X³). (b) Find (i) the variance, (ii) the standard deviation for the random variable of X.
solve only 4 and 5 plz
Q6
B1. Let X be a continuous random variable with PDF 2 f(x) = ½ ½ (2 - x) 9 and f(x) = 0 otherwise. for 1x c (a) Explaining your work, find the value of the constant c. (b) What is P(X > 1)? (c) Calculate the expectation of X. (d) Calculate the variance of X
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