Page 189 - Engineering Mathematics Workbook_Final

Probability & Statistics

 1  10 158. Among 10,000 random digits, find
−
(a) e + − 2       (1 e − 2 ) the probability that the digit 3 appears
 4 
atmost 950 times. (Area under normal
 1  10 curve between Z = 0 and Z = 1.67 is
−
(b) e + − 2       (1 2e − 2 ) 0.4525)
 4 
Exponential Distribution
 1  10
(c) e − 1       159. A continuous random variable X has
 4 
probability density function given by
 1  10

(d) e + − 2 1−        2e − 2x x  0
 4  f ( ) x =  0, otherwise


Normal (Gaussian) Distribution
The mean and variance of X are
156. For a random variable
1 1
1 1
)
x
X (−   following normal (a) , (b) ,
distribution, the mean is  = 100. If 2 8 2 4
=
the probability is P  for x  110. 1 1
Then the probability of x lying (c) 1, (d) 2,
2
2
between 90 & 110 i.e;
P (90  x  110 ) and equal to 160. If X is exponentially distributed, the
probability that X exceeds its
−
(a) 1 2 (b) 1 − expected value is _______

 161. The length of the shower on a tropical
(c) 1− (d) 2 island during rainy season has an
2
exponential distribution with
157. If the masses of 300 students are parameter 2, time being measured in
normally distributed with mean 68 minutes. What is the probability that
kgs and standard deviation 3 kgs. a shower will last more than 3 min?

How many students have masses
Uniform Distribution
(i) Greater than 72 kg
162. A random variable X is uniformly
(ii) Less than or equal to 64 kg distributed in the interval [0,1]. Find

(iii) between 65 & 71 kg (both (i) E(X) (ii) ( )
E X
2
inclusive)
3
E X
(iii) ( ) (iv) Variance
(Area under normal curve between Z
= 0 & Z = 1.33 is 0.4082)

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