Page 192 - Engineering Mathematics Workbook_Final

Probability & Statistics


of 8.9 years. Use 5% level of (d) ( A B = + +
P
) 1 p q
significance. z = z = 1.645 
 0.05
178. Let X be a random variable with the
175. The mean life time of a sample of 25 cumulative distribution function
bulbs is found as 1550 hours with a 
standard deviation of 120 hours. The  0, for x  0

1 x
company manufacturing the bulbs  + 2 for 0  x  1

claims that the average life of their  10


bulbs is 1600 hours. Is the claim F ( ) x =  3 x 2
+

acceptable at 5% loss?  10 for  1 x  2

t − 0.05 for 24 dof = 1.71 .  1, for x  2


1 1
176. If ( ) A = and ( ) = , then Which of the following statements is
P B
P
3 4 (are) TRUE?
which of the following is correct?
3

P
1 (a) (1 X  ) 2 =
)

(a)  P ( A B 10
3
3

P
1 (b) (1 X  ) 2 =
)
(b)  P ( A B 5

3
1
P 
) 2 =
(c) (1 X 


P
(c) ( A B  ) 1 2
12
4
(d) (1 X 
) 2 =
P 

P
(d) ( A B  ) 1 5
3
[JAM MS 2019]
177. The probability of the simultaneous
occurrence of two events A and B if 179. Let P be a probability function that
p. If the probability that exactly one assigns the same weight to each of
of A and B is q. Then which of the the points of the sample space
following is correct?  = 1,2,3,4. Consider the events
E =  , F =   and G =  
1,3
3,4
1,2
( ) ( )
(a) P A + P B = − − . Then which of the following
2 2p q
(
−
−
(b) P A B ) = 1 p q statement(s) is (are) true?
(a) E and F are independent
p (b) E and G are independent
P
(c) ( A B A B /  ) =
+
p q
(c) F and G are independent

190