This preview shows page 1. Sign up to view the full content.
Homework Assignment 1:
(1) Let f(x) =
a
(e
2x
– e
3x
) for x
≥
0 and 0 elsewhere.
Find the constant
a
so that f(x) satisfies the
conditions of being a probability density function.
Calculate Pr(X
≤
1).
(Ans
a
= 6; Pr(X
≤
1) = 0.6936)
(2) Let f(x) = 1.5x + .25, 0
≤
x
≤
1, zero elsewhere, be the probability density function of X.
Find the distribution function of X and calculate Pr ( ¼
≤
X
≤
¾).
(Ans F(x) = 0 for x < 0, .75x
2
+ .25x for 0
≤
x
≤
1 and 1 for x > 1.
Pr( ¼
≤
X
≤
¾) = 0.5)
(3) You play a slot machine repeatedly.
The probability of winning on a single play is 0.05,
and successive plays are independent.
Let X be the random variable for the number of
unsuccessful attempts before the first win.
Find F(x) for x = 0,1,2,… , and determine
how many times you would need to play the slot machine in order to be sure that your
probability of winning at least once is 99%.
(Ans. F(x) = 1  .95
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 CharlesDann

Click to edit the document details