f(x₁, x₂) = {1,- ([1-a(1-2e-x₁)(1-2e-x₂)]ex₁-x2 otherwise ,0 ≤ x₁,0 ≤ x₂. 0, i) Find the marginal distribution of X₁. ii) Find E(X₁X₂). b) Consider a random variable K with parameter p, whose probability mass function (PMF) is given by f(k) = {* elsewhere k=1,2,. lo, i) Derive the moment generating function of K. ii) Use the result obtained in i), to find the expected value of K. iii) Use the result obtained in i), to find the variance of value of K. c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and standard deviation 4. Suppose that X and Y are independent, use an appropriate method to determine his probability distribution of the random variable X + Y.
f(x₁, x₂) = {1,- ([1-a(1-2e-x₁)(1-2e-x₂)]ex₁-x2 otherwise ,0 ≤ x₁,0 ≤ x₂. 0, i) Find the marginal distribution of X₁. ii) Find E(X₁X₂). b) Consider a random variable K with parameter p, whose probability mass function (PMF) is given by f(k) = {* elsewhere k=1,2,. lo, i) Derive the moment generating function of K. ii) Use the result obtained in i), to find the expected value of K. iii) Use the result obtained in i), to find the variance of value of K. c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and standard deviation 4. Suppose that X and Y are independent, use an appropriate method to determine his probability distribution of the random variable X + Y.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![a) Suppose that, for −1≤ a ≤ 1, the probability density function of (X₁, X₂) is given by
f(x₁, x₂) = {11-
([1-α(1 - 2e-x₁)(1-2e-x²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).
b) Consider a random variable K with parameter p, whose probability mass function (PMF) is
given by
f(x) = { pak k = 1.,2., .......
elsewhere
i) Derive the moment generating function of K.
ii) Use the result obtained in i), to find the expected value of K.
iii) Use the result obtained in i), to find the variance of value of K.
c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc219a71-a3f3-49e8-b112-638d327202a9%2F83f02a26-8f2f-4956-83e9-dd9b8a47e0c3%2Fymem5pi_processed.png&w=3840&q=75)
Transcribed Image Text:a) Suppose that, for −1≤ a ≤ 1, the probability density function of (X₁, X₂) is given by
f(x₁, x₂) = {11-
([1-α(1 - 2e-x₁)(1-2e-x²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).
b) Consider a random variable K with parameter p, whose probability mass function (PMF) is
given by
f(x) = { pak k = 1.,2., .......
elsewhere
i) Derive the moment generating function of K.
ii) Use the result obtained in i), to find the expected value of K.
iii) Use the result obtained in i), to find the variance of value of K.
c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + Y.
![a) Suppose that, for −1≤ a ≤ 1, the probability density function of (X₁, X₂) is given by
f(x₁, x₂) = {11-
([1-α(1 - 2e-x₁)(1-2e-x²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).
b) Consider a random variable K with parameter p, whose probability mass function (PMF) is
given by
f(x) = { pak k = 1.,2., .......
elsewhere
i) Derive the moment generating function of K.
ii) Use the result obtained in i), to find the expected value of K.
iii) Use the result obtained in i), to find the variance of value of K.
c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + Y.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbc219a71-a3f3-49e8-b112-638d327202a9%2F83f02a26-8f2f-4956-83e9-dd9b8a47e0c3%2Ffwvdxp_processed.png&w=3840&q=75)
Transcribed Image Text:a) Suppose that, for −1≤ a ≤ 1, the probability density function of (X₁, X₂) is given by
f(x₁, x₂) = {11-
([1-α(1 - 2e-x₁)(1-2e-x²)]ex1-x2
otherwise
,0 ≤ x₁,0 ≤ x₂.
i) Find the marginal distribution of X₁.
ii) Find E(X₁X₂).
b) Consider a random variable K with parameter p, whose probability mass function (PMF) is
given by
f(x) = { pak k = 1.,2., .......
elsewhere
i) Derive the moment generating function of K.
ii) Use the result obtained in i), to find the expected value of K.
iii) Use the result obtained in i), to find the variance of value of K.
c) Mr Ledwaba from Department of Health assumed that a random variable X is normal with
mean 2 and standard deviation 3 and that random variable Y is normal with mean 0 and
standard deviation 4. Suppose that X and Y are independent, use an appropriate method
to determine his probability distribution of the random variable X + Y.
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