(i) We construct the following table to find the expected value, variance, and standard deviation :
![](https://www.sarthaks.com/?qa=blob&qa_blobid=8606213657289932632)
From the table,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10149805175163157381)
(ii) We construct the following table to find the expected value, variance, and standard deviation:
xi |
P(xi) |
xi.P(xi) |
xi2.P(xi) = xi × xi.P(xi) |
-1 |
1/5 |
- 1/5 |
1/5 |
0 |
2/5 |
0 |
0 |
1 |
2/5 |
2/5 |
2/5 |
Total |
1 |
1/5 |
3/5 |
From the table,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10387409995935462956)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=14611137076064307972)
(iii) We construct the following table to find the expected value, variance, and standard deviation:
![](https://www.sarthaks.com/?qa=blob&qa_blobid=4690688256150431685)
From the table,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=11660503972903583491)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=4280391528780211588)
![](https://www.sarthaks.com/?qa=blob&qa_blobid=15618074568800132584)
(iv) We construct the following table to find the expected value, variance, and standard deviation:
xi |
P(xi) |
xi.P(xi) |
xi2.P(xi) = xi × xi.P(xi) |
0 |
1/32 |
0 |
0 |
1 |
5/32 |
5/32 |
5/32 |
2 |
10/32 |
20/32 |
40/32 |
3 |
10/32 |
30/32 |
90/32 |
4 |
5/32 |
20/32 |
80/32 |
5 |
1/32 |
5/32 |
25/32 |
Total |
32/32 |
80/32 |
240/32 |
From the table,
![](https://www.sarthaks.com/?qa=blob&qa_blobid=10883783916753159534)