Let X~BIN(40,0.1). Let Y=max(0,x-3). FindE[Y].

Expert Solution

Since X is binomially distributed over (40,0.1), i calculated the distribution using calculation and table is given below:

Binomial distribution (n=40, p=0.1)
	f(x)
x	Pr[X = x]
0	0.0148
1	0.0657
2	0.1423
3	0.2003
4	0.2059
5	0.1647
6	0.1068
7	0.0576
8	0.0264
9	0.0104
10	0.0036
11	0.0011
12	0.0003
13	0.0001
14	0
15	0
16	0
17	0
18	0
19	0
20	0
21	0
22	0
23	0
24	0
25	0
26	0
27	0
28	0
29	0
30	0
31	0
32	0
33	0
34	0
35	0
36	0
37	0
38	0
39	0
40	0

Now Y = max (0, x-3).

This means that,

Y = 0, for all x 3

Y = x-3. for all x 4

Y	x	P(x)	*YP(x)**
0	0	0.0148	0
0	1	0.0657	0
0	2	0.1423	0
0	3	0.2003	0
1	4	0.2059	0.2059
2	5	0.1647	0.3294
3	6	0.1068	0.3204
4	7	0.0576	0.2304
5	8	0.0264	0.132
6	9	0.0104	0.0624
7	10	0.0036	0.0252
8	11	0.0011	0.0088
9	12	0.0003	0.0027
10	13	0.0001	0.001
11	14	0	0
12	15	0	0
13	16	0	0
14	17	0	0
15	18	0	0
16	19	0	0
17	20	0	0
18	21	0	0
19	22	0	0
20	23	0	0
21	24	0	0
22	25	0	0
23	26	0	0
24	27	0	0
25	28	0	0
26	29	0	0
27	30	0	0
28	31	0	0
29	32	0	0
30	33	0	0
31	34	0	0
32	35	0	0
33	36	0	0
34	37	0	0
35	38	0	0
36	39	0	0
37	40	0	0
		Sum=	1.3182

Now E[Y] = Y * P(x)

E[Y] = 1.3182

orchestra answered 2 years ago

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