Page 209 - Engineering Mathematics Workbook_Final

Probability & Statistics

286. A probability distribution with right (a) 0 (b) 0.5
skew is shown in the figure.
(c) 1 (d) 10

[GATE-2008 (IN)]

289. The cumulative distribution function
of a random variable x is the
probability that X takes the value

(a) less than or equal to x
The correct statement for the
probability is distribution is (b) equal to x

(a) Mean is equal to mode (c) greater than x

(b) Mean is greater than median but (d) zero [ESE 2017 (EC)]
less than mode 290. The probability density function

(c) Mean is greater than median and F ( ) x = ae − b x where x is a random
mode variable whose allowable value range

(d) Mode is greater than median is from x = − to x = +. The CDF
for this function for x  0 is
[GATE 2018 (CE-AFTERNOON
a
a
SESSION)] (a) e (b) (2 e − bx )
−
bx
b b
,
287. Let X 1 , X X and X be
4
3
2
a
independent normal random variables (c) − a e (d) ( 2 e − bx )
bx
−
+
with zero mean and unit variance. b b
The probability that X is the [ESE 2017 (EC)]
4
smallest among the four is _______.

[GATE-2018 (EC)]
CUMMULATIVE DISTRIBUTION
FUNCTION

288. Consider a Gaussian distributed
random variable with zero mean and
standard deviation  . The value of
its cumulative distribution function at
the origin will be

207