For the following discrete distribution X PX CDF 1 007 2 016

For the following discrete distribution:

X

P(X)

CDF

1

0.07

2

0.16

3

0.14

4

0.18

5

0.25

6

0.20

a) Write the CDF in the table.

b) Find E(X).

c) Suppose the result of a six is considered a success. If the experiment was repeated until 5 successes

    (sixes) were recorded. What is the expected number of TRIALS?

d) What type of experiment is described in part c)?

e) What is the probability of exactly 2 sixes in 5 trials?

f) What is the expected number of sixes in 5 trials?

g) What is the variance for the number of sixes in 5 trials?

Solution

a)

Adding up the P(x) values up to that row, we get the cdf:

b)

Consider:

Thus, E(x) = 3.98 [ANSWER]

******************************

c)

Here, it is a negative binomial process, where x = the number of successes, p = probability of success.

Expected number of trials = x/p = 5/0.2 = 25 [ANSWER]

d)

It is a negative binomial experiment.

*******************************************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Please indicate which parts are not yet solved when you submit. Thanks!