SECTION B Question 1 Suppose X is a random variable with the following probability density function g(x) = k(x²+1), 00.4) d) Hence find the mean and variance of Y = 2-3x. [2] [4] [4] [6] [4] Question 2 Let X and Y be random variables with the probability density function and moment generating function given respectively by H(x)= , x = 0,2,4 and mx My(t) = (1-21)+, 0 ≤1≤ a) Find the value of m. b) Evaluate P(0≤t<3). c) Find the mean and variance of X. [2] [3] [5] d) Find the mean and variance of Y. [5] e) If X and Y are dependent random variables with covariance σxy = 0.2 find mean and variance of the random variable Z=2X-3Y+5. 2 [5]
SECTION B Question 1 Suppose X is a random variable with the following probability density function g(x) = k(x²+1), 00.4) d) Hence find the mean and variance of Y = 2-3x. [2] [4] [4] [6] [4] Question 2 Let X and Y be random variables with the probability density function and moment generating function given respectively by H(x)= , x = 0,2,4 and mx My(t) = (1-21)+, 0 ≤1≤ a) Find the value of m. b) Evaluate P(0≤t<3). c) Find the mean and variance of X. [2] [3] [5] d) Find the mean and variance of Y. [5] e) If X and Y are dependent random variables with covariance σxy = 0.2 find mean and variance of the random variable Z=2X-3Y+5. 2 [5]
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
Related questions
Question
![SECTION B
Question 1
Suppose X is a random variable with the following probability density function
g(x) = k(x²+1), 0<x<1
a) Find the value of k.
b) Find the distribution function G(x) = P(X ≤ x).
d) Find the mean and variance of X.
c) Evaluate (i) P(-1<X<0.6) (ii) P(X>0.4)
d) Hence find the mean and variance of Y = 2-3x.
[2]
[4]
[4]
[6]
[4]
Question 2
Let X and Y be random variables with the probability density function and
moment generating function given respectively by
H(x)=
, x = 0,2,4
and
mx
My(t) = (1-21)+, 0 ≤1≤
a) Find the value of m.
b) Evaluate P(0≤t<3).
c) Find the mean and variance of X.
[2]
[3]
[5]
d) Find the mean and variance of Y.
[5]
e) If X and Y are dependent random variables with covariance σxy = 0.2
find mean and variance of the random variable Z=2X-3Y+5.
2
[5]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2006393e-c97e-4081-8173-0190425f3dd9%2Fd8aa3109-a759-4d1e-af72-8b81729f5f5c%2Fzbwd7ue_processed.jpeg&w=3840&q=75)
Transcribed Image Text:SECTION B
Question 1
Suppose X is a random variable with the following probability density function
g(x) = k(x²+1), 0<x<1
a) Find the value of k.
b) Find the distribution function G(x) = P(X ≤ x).
d) Find the mean and variance of X.
c) Evaluate (i) P(-1<X<0.6) (ii) P(X>0.4)
d) Hence find the mean and variance of Y = 2-3x.
[2]
[4]
[4]
[6]
[4]
Question 2
Let X and Y be random variables with the probability density function and
moment generating function given respectively by
H(x)=
, x = 0,2,4
and
mx
My(t) = (1-21)+, 0 ≤1≤
a) Find the value of m.
b) Evaluate P(0≤t<3).
c) Find the mean and variance of X.
[2]
[3]
[5]
d) Find the mean and variance of Y.
[5]
e) If X and Y are dependent random variables with covariance σxy = 0.2
find mean and variance of the random variable Z=2X-3Y+5.
2
[5]
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