Page 199 - Engineering Mathematics Workbook_Final

Probability & Statistics

the probability that the locks can still 1
opened by drawing one key at (c) 18 (d) none of these
random is equal to RANDOM VARIABLE
1 5
(a) (b) 220. Let X and Y be two independent
3 6 random variables. Which one of the
1 1 relations between expectation ©,
(c) (d) variance (Var) and covariance (Cov)
12 30
[GATE] given below is FALSE?
)
E
( ) ( )
216. A party of n persons takes their seats (a) ( XY = E X E Y
at random at a round table, then the (b) Cov X ) 0
( ,Y =
probability that two specified person © Var X + Y = ( ) Var Y
(
( )
) Var X +
do not sit together is
2
2 n − 3 (d) ( X Y 2 ) (E X 2 ( ))
=
2
( )) (E Y
E
(a) (b)
n − 1 n − 1 [GATE-2007-ME]
n − 2 1 221. If the standard deviation of the spot
(c) (d)
n − 1 n − 1 speed of vehicles in a highway is
[GATE] 8.8km/h and the mean speed of the
217. The letters of the word vehicles is 33 km/h, the coefficient of
PROBABILITY are arranged in all variation in speed is
possible ways. The chance that B’s (a) 0.1517 (b) 0.1867
and also two I’s occur together is © 0.2666 (d) 0.3646
1 2 [GATE-2007-CE]
(a) (b) 222. If the difference between the
55 55 expectation of the square of a random
4  2 

(c) (d) none of these variable ( ) E X and the square of
165  
218. From 6 positive and 8 negative the expectation of the random

( )
numbers 4 numbers are drawn at variable E X    2 is denoted by R,


random without replacement and then
multiplied, the probability that the (a) R = 0 (b) R < 0
product is a positive number is © R  0 (d) R > 0
505 50
(a) (b) [GATE-2011 (CS)]
1001 1001 223. A simple random sample of 100
5 55 observations was taken from a large
(c) (d)
101 1001 population. The sample mean & the
[GATE] standard deviation were determined
219. If two squares are chosen at random to be 80 to 12 respectively. The
on a chess board to probability that standards error of mean is ______
they have a side in common is [GATE-2014 (PI-SET1)]
1 2
(a) (b)
9 7

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