SOLUTION: Given the following probability mass function, 𝑓(𝑥) = 𝑃(𝑋 = 𝑥) = 𝑐(2𝑥 − 1) for x=1,2,3 determine which of the statements below are true. I. The value of c

Question 1187262: Given the following probability mass function, 𝑓(𝑥) = 𝑃(𝑋 = 𝑥) = 𝑐(2𝑥 − 1) for x=1,2,3
determine which of the statements below are true.
I. The value of c is
1
3
.
II. The Expected value of the distribution is 2.44 (to 2 decimal places).
III.
P X( 1) 0.67  
(to 2 decimal places).
A. Only statements I and III are true.
B. Only statement II is true.
C. Only statements II and III are true.
D. Only statement III is true.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

I.
P(1) = c(2-1) = c
P(2) = c(4-1) = 3c
P(3) = c(6-1) = 5c

P(1)+P(2)+P(3) = c+3c+5c = 1; 9c=1; c=1/9

I. is FALSE

II.
The expected value is
(1/9)(1)+(3/9)(2)+(5/9)(3) = 22/9 = 2.44 (rounded)

II. is TRUE

III.
I don't know what this part says....

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