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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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.
Transcribed Image Text: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.
Expert Solution
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:

Statistics homework question answer, step 2, image 1

Thus, the value of c so that f (x) is a pdf, is n (n + 1) / 2.

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