Question

Question 1

The random variable X is a payout table of a casino slot machine. The probability mass function is given:

X   -5   0   2   10   20   40   60   1000
Probability   0.65   0.159   0.10   0.05   0.02   0.01   0.01   0.001
Find the standard deviation of the payout .

Question 2

The random variable X is a payout table of a casino slot machine. The probability mass function is given:

X   -5   0   2   10   20   40   60   1000
Probability   0.65   0.159   0.10   0.05   0.02   0.01   0.01   0.001
Please simulate the results for playing the slot machine 10,000,000 times. Find the mean of these 10,000,000 simulated payout outcomes .

Question 3

In twenty prey visits on carnivorous plants, if the probability of a capture in one visit is 0.2, what is the probability to have 3 to 6 captures ,
or P(3 less or equal than X less or equal than 6).

Question 4

If the probability of a capture is 0.2 when a prey visits on carnivorous plants, find is the probability that there are 5 or more visits until the 3 captures.
Hint: negative binomial, and find prob that the number of failures (no captures) is 2 or more.
1 - P( the number of no captures is no more than 1)

Please help solve these last four questions I have. They must be calculated using R.

Answer 1

1)

x	P(x)	x * P(x)	x2 P(x)
-5	0.65	-3.25	16.25
0	0.159	0	0
2	0.1	0.2	0.4
10	0.05	0.5	5
20	0.02	0.4	8
40	0.01	0.4	16
60	0.01	0.6	36
1000	0.001	1	1000
Sum	1	-0.15	1081.65

Mean = X * P(X)

= -0.15

Standard deviation =

=X ² * P(X) - ²

=  1081.65 -(-0.15)²

= 32.89

standard deviation of the payout = 32.89