Let X be a discrete random variable with possible values {0, 1, 2, ...} and the following probability mass function: P(X=0)=4/5 and for k€{1, 2, 3, ...} P(X=k)=1/10*(2/3)^k. a. Verify that the above is a probability mass function. b. For k€{1, 2, ...}, find P(X>k|X>1).
Let X be a discrete random variable with possible values {0, 1, 2, ...} and the following probability mass function: P(X=0)=4/5 and for k€{1, 2, 3, ...} P(X=k)=1/10*(2/3)^k. a. Verify that the above is a probability mass function. b. For k€{1, 2, ...}, find P(X>k|X>1).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 20E
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Let X be a discrete random variable with possible values {0, 1, 2, ...} and the following
a. Verify that the above is a probability mass function.
b. For k€{1, 2, ...}, find P(X>k|X>1).
Expert Solution
Step 1
We have been given that,
P(X=0) = 4/5 and for k ∈ {1, 2, 3...} we have,
Part a:
To show that the given mass function is a probability mass function we need to sow that total probability is equal to 1.
Thus, we have,
Thus, we have total probability = 1.
Hence, above given mass function is a probability mass function.
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