00:01
So here the exponential probability distribution function of exponential distribution function, f of x is given as theta e power minus theta x, where x greater than are equal to 0.
00:12
Also we have mean of x is equal to 1 by theta, so which is 10 from this theta equal to 1 by 10.
00:20
Now the first question is we have to find the probability density function of x.
00:25
So which implies f of x is equal to 1 by 10 e power minus x by 10 per x greater than equal to 0.
00:34
Then second question, we have to find p of x less than 20, which is equal to integral over x, f of x d x, which is integral 0 to 20, 1 by 10, e power minus x by 10 dx, which is 1 by 10 times e power minus x by 10, divot by 10, divided by, minus 1 by 10 from 0 to 20.
00:59
So which is minus of e power minus 20 by 10 minus e power minus 0 minus 0 minus 2 plus 1, which is equal to 1 minus 0 .133 which is 0 .8647.
01:23
Hence p of x less than 20 is 0 .8647...