Question

Here is a value randomly generated from a uniform distribution on the interval [0,1]: 0.58814 10. If we wanted to use this value to generate an observation from a random variable X having an exponential distribution with @ = 7, what would be corresponding value of x? (Round to three decimal places.)

Answer 1

Pq No to Answert Given datar there is a value randomly generated from a uniform distribution on the interval [o,i). To generate an oblovation from a random variable x exponential distribution with 0-7. Iverse transformation technique can be wed here tet u. be a uniform Random variable Pr. the range [oi]. If x=F-' (u); Then x lů a Random variable with - CDF Ex(x) = F. i fxra) = P [x <a] - P[f-'(u) <a]=P [U = f(aj] = f(a) . x ů an Sponential variable with >=7 . Then, COF. of x i f(x) = l-e-dk.

Here calculated x as x 1. = f'(U) - - In (1-4) Now, we have u= 0158814. X-7 in the substituting the wand a values above above equation. X=-in (l-) - In (Y-0.58814) sin (0.41186) --5-0.887 = 0.1267 1: X=0.1967 1