Probability distribution/Miscellenious Exercise Mcq's/ class 12 mh board
(1) P.d.f. of a.c.r.v X is f (x) = 6x (1 − x), for
x belongs to [0 1] and = 0, otherwise (elsewhere)
If P (X is less than a) = P (X is greater than a), then a =
(A) 1
(B)
1/2
(C)
1/3
(D)
1/4
(2) If the p.d.f of a.c.r.v. X is f (x) = 3 (1 − 2x²), for x belongs to [0 1] and = 0, otherwise (elsewhere)
then the c.d.f of X is F(x) =
(A) 2x − 3x² (B) 3x − 4x³ (C) 3x − 2x³ (D) 2x³ − 3x
(3) If the p.d.f of a.c.r.v. X is f (x) = x2
18 , for x belongs to (-3 3) and = 0, otherwise
then P (| X | less than 1) =
(A)
1/27 (B)
1/28 (C)
1/29 (D)
1/26
(4) If a d.r.v. X takes values 0, 1, 2, 3, . . . which probability P (X = x)=k (x + 1)·5^−x
, where k is
a constant, then P (X = 0) =
(A)
7/25 (B)
16/25 (C)
18/25 (D)
19/25
(5) If p.m.f. of a d.r.v. X is P (X = x) = 5Cx
/
2^5, for x = 0, 1, 2, 3, 4, 5 and = 0, otherwise
If a = P (X is less than equal to 2) and b = P (X is greater than equal to 3), then
(A) a is less than b
(B) a is greater than b
(C) a = b
(D) a + b