Answer to Question #125175 in Statistics and Probability for Mohammad Bilal Farooq Qureshi

Question

13. If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A|B) is:
14 If set ‘A’ and set ‘B’ have some common elements then it will be written as
15 If there is not any common elements in two sets A and B then they are
16 If x ~ N (100, 100) then points of inflection are
17 If x ~ N (25, 64) then mean and standard deviation of normal distribution respectively are
18 If X and Y are independent random variables then E(XY) is equal to
19 If x and y are independent random variables then Var (3x – y) =
20 If x and y are independent random variables then Var (x + y) =

Answer 1

13. P(A/B)=P(A and B)/P(B)= 0.25/0.35=0.714

14.A $\bigcap$ B

15.disjoint

16.point of infection in normal distribution is given by mean -sd and mean + sd .Hence here point of infection is 100- 10, 100+10. That is 90 and 110

17.Normal distribution follows N(mean, variance)

Hence mean = 25, sd = 8

18.when x and y are independent E(XY)=E(X)E(Y).

19.When x and Y are independent .Var (ax-by)= a^2 Var(x)+b^2 Var(y)

Hence Var(3x-y)=3^2Var(x)+1^2Var(Y)

=9Var(x)+var(Y)

20: when X and y are independent Var (ax+by)= a^2Var (x)+b^2Var(Y)

Var(x+y)= 1^2Var(x)+1^2var(y)

=Varx+var(y)