x/c x= 1,2,n Suppose that f(x) = • otherwise Find c so that f(x) represents a pdf. Find an expression for the CDF, F (x). Find E(X). а. b. с.
x/c x= 1,2,n Suppose that f(x) = • otherwise Find c so that f(x) represents a pdf. Find an expression for the CDF, F (x). Find E(X). а. b. с.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 51E
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Step 1
Introduction:
For a discrete random variable X, the probability mass function or probability distribution function (pdf) must satisfy the following condition:
- For each value x taken by the random variable X, 0 ≤ f (x) ≤ 1.
- The sum of f (x) taken over all possible values x is, Σ f (x) = 1.
Step 2
a.
Here, the random variable is X. The value of c must be such that, Σ f (x) = 1, when the summation is taken over all values of x = 1, 2, …, n. The value of c is calculated below:
Thus, the value of c so that f (x) is a pdf, is n (n + 1) / 2.
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