Expectations
Question
1/2
Q1.
Find the value of V(5) .
(a) 0
(b) 1
(c) 2
(d) 3
Solution. a
∴ v(a) = 0
Where a is any constant .
Solution
Q2.
Covariance (x,x) = _______________ .
(a) Variance of x
(b) Mean of x
(c) 0
(d) None of these
Solution.a
Cov(x,y) =
1/n
∑ (x - x̅)
(y - y̅)
Cov(x,x) =
1/n
∑ (x - x̅)
2
Solution
Q3.
A coin is tossed 3 times , X is a random variable getting head . Find expectation of getting head .
(a) 1
(b) 1.5
(c)2
(d) 2.5
Solution.b
| x |
0 |
1 |
2 |
3 |
| P(x) |
1/8 |
3/8 |
3/8 |
1/8 |
Note : As we know that in this case possible values of random variable x is 0,1,2,3 .
Formula to find expectation
= ∑ x . P(x)
So its answer is 1.5
Solution
Q4.
| x |
0 |
1 |
2 |
3 |
| P(x) |
1/8 |
3/8 |
1/8 |
2/8 |
Check it is p.d.f or not .
(a) Its a p.d.f
(b) Not a p.d.f
(c) can't say
(d) None of these
Solution. b
(i) All probabilities should be non negative .
(ii) Sum of all the probabilities should be equal to 1 .
A distribution will be p.d.f if it is satisfied both the conditions .
So in this case second condition is not satisfied , this is why it is not a p.d.f
Solution
Q5.
A bag contains 3 white and 2 black ball . A person selects two balls at random . Find the expected number of black balls.
(a) 0.8
(b) 0.9
(c) 1
(d) 1/2
Solution.a
| No. of balack balls |
P(x) |
x . P(x) |
| 0 |
3/10 |
0 |
| 1 |
6/10 |
6/10 |
| 2 |
1/10 |
2/10 |
So expected number of black balls E(x) = ∑ x . P(x) = 8/10
Solution
