00:01
Hello students, in this question by using the given pdf we have to calculate the following probabilities.
00:06
So, first we have to calculate a probability of x is less than or equal to 4.
00:11
This is equal to now the range of x is from 1 to up to infinity.
00:16
So, we have to calculate probability of x is less than or equal to 4.
00:20
That means integration is from 1 to up to 4 f of x dx that is equal to now integration from 1 to up to 4 0 .45 into e raised to minus 0 .45 into x minus 1 dx and here 0 .45 is constant.
00:42
So, we can take it outside the integration then integration from 1 to up to 4 e raised to minus 0 .45 into x minus 1 dx and we know that integration of e raised to x is e raised to x.
00:56
So, this is 0 .45 into e raised to minus 0 .45 into x minus 1 divide by the derivation of minus 0 .45 into x minus 1 is minus 0 .45 and limits from 1 to up to 4.
01:16
Then this is equal to 0 .45 and 0 .45 will get cancelled.
01:22
So, minus 1 into bracket now upper limit minus lower limit that is e raised to minus 0 .45 into bracket 4 minus 1 minus e raised to minus 0 .45 into bracket 1 minus 1 and that is equal to after simplifying this we will get minus 1 into bracket 0 .2592 minus 1 that is the required probability is equal to 0 .741...