Question

er Select your ans b. What is the probability of generating a random number between 0.15 and 0.75 (to 1 decimals)? c. What is the probability of generating a random number with a value less than or equal to 0.3 (to 1 decimals) ? d. What is the probability of generating a random number with a value greater than 0.7 (to 1 decimals)? e. Using 50 random numbers given below, compute the mean and standard deviation. 0.220487 0.753376 0.925566 0.178574 0.625610 0.640926 0.241717 0.945829 0.899303 0.629137 0.378775 0.344095 0.138804 0.768202 0.922997 0.410529 0.188698 0.259897 0.718625 0.512393 0.530289 0.344440 0.456399 0.200510 0.347524 0.641231 0.347192 0.270934 0.277986 0.323283 0.601512 0.022542 0.199379 0.073149 0.012108 0.557077 0.245750 0.598994 0.196649 0.732452 0.698506 0.068024 0.837645 0.549681 0.305418 0.513275 0.343656 0.302708 0.100656 0.421961 (to 6 decimals) Mean = (to 6 decimals) Standard deviation -

Answer 1

A random number by default is always drawn from an Uniform(0,1) distribution.When we need random number from any other distribution,necessary transformation are made.Hence,if X is a random number,then X~U(0,1)

Then,the pdf of X is

fx(c) = 1 if (<x<1 o if o.w.

and,the cdf of X is

o P[X < x] = Fx(x) = { 11 if < 0 if 0<x< 1 if r>1

b.

P(0.15 < X < 0.75] = Fx(0.75) - Fx(0.15) = 0.75 -0.15 = 0.6

c.

PLX < 0.31 = Fx(0.3) = 0.3

d.

P[X > 0.7) = 1 - P[X < 0.7] = 1 – Fx(0.7) = 1 -0.7 = 0.3

e.

= Mean, 1 = 1-2

and,

sd, s= 1-0 (ri - .)2

Here,n=50.Here,x_i are the random numbers.

Mean, I = Ti = 0.436489

and,

sd, s= (P; - 0.436489)2 = 0.254223