Question

The following table shows part of the probability distribution for the number of boats sold daily at Boats Unlimited. It is known that the average number of boats sold daily is 1.57. x f(x) 0 0.20 1 0.30 2 0.32 3 ? 4 0.05 5 ? Complete the distribution by computing the probabilities of selling 3 nd 5 boats per day.

All boats sell for $2000. What is the standard deviation of the daily revenue of the company?

Answer 1

Since for a valid pdf sum of probabilities must be equal to 1 so

Now,

................(1)

It is given that expected value is 1.57 so

Now,

................(2)

Now multiply equation (1) by 3 and subtract it from equation (2) gives

Now putting this in equation (1) gives

Following is the completed table:

X	f(x)
0	0.2
1	0.3
2	0.32
3	0.11
4	0.05
5	0.02
Total	1

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Following table shows the calculations for SD:

X	f(x)	xf(x)	x^2*f(x)
0	0.2	0	0
1	0.3	0.3	0.3
2	0.32	0.64	1.28
3	0.11	0.33	0.99
4	0.05	0.2	0.8
5	0.02	0.1	0.5
Total	1	1.57	3.87

So,

Let Y shows the total revenue. So

Y = 2000*x

Therefore the standard deviation of the daily revenue of the company will be