Page 193 - Engineering Mathematics Workbook_Final

Probability & Statistics

(d) E, F and G are independent 1
(a) c =
[JAM MS 2018] 8


180. Let S be the set of all 3 3 matrices (b) c = 8
having 3 entries equal to 1 and 6 (c) X and Y are independent
entries equal to 0. A matrix M is
picked uniformly at random from the (d) P (X = Y) = 0 [NET JUNE
set S. Then 2017]

:
1 183. Let X i   1 be a sequence of
i
(a) P { M is nonsingular } =
14 independent random variables each
having a normal distribution with
1
(b) P { M has rank 1 } = mean 2 and variance 5. Then which
14 of the following are true

1 1 n
(c) P { M is identity } = (a)  X converges in probability
14 i n 1 = i

1 to 2.
(d) P { trace (M) = 0 } =
14 1 n
2
(b)  X converges in probability
i
181. Suppose A, B, C are events in a i n 1 =
common probability space with P(A) to 9.

= 0.2, P(B) = 0.2, P(C) = 0.3,   2


P ( A B = ) 0.1, P ( A C = ) 0.1, (c)   1 i n n X i      converges in

P (B C = ) 0.1. Which of the  1 = 
probability to 4.
following are possible values of
P ( A B C  )? n   X i   2
(d)      converges in
i= 1  n 
(a) 0.5 (b) 0.3
probability to 0.
(c) 0.4 (d) 0.9
[NET DEC 2016]

182. Let c R be a constant. Let X, Y be 184. A and B are two events defined as
random variables with joint follows:
probability density function
A: It rains today with P(A) = 40%
 cxy for 0 x   1

y

)
f ( ,x y =  .
 0 otherwise B: It rains tomorrow with P(B) = 50%

Which of the following statements Also, P(it rains today and tomorrow)
are correct? = 30%

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