 Hi and welcome to the session. Let's work out the following question. The question says for a poison distribution it is given that probability at x equals to 1 is equal to probability at x equal to 2. Find the value of mean of the distribution hence find probability x equal to 0 and probability at x equal to 4 using e raised to power minus 2 is equal to 0.13534. Let us see the solution to this question. First of all let the probability distribution of x be given by probability at x equal to r is equal to m raised to power r into e raised to power minus m divided by r factorial where r is equal to 0, 1, 2, 3 and so on and we call this equation 1. Therefore probability at x equal to 1 will be equal to m raised to power 1 into e raised to power minus m divided by 1 factorial that is m into e raised to power minus m and probability at x equals to 2 is equal to m square into e raised to power minus m divided by 2. But according to the question probability at x equal to 1 is equal to probability at x equal to 2. This implies m into e raised to power minus m is equal to m square into e raised to power minus m divided by 2. This implies that m is equal to 2. Now putting the value of m that is m equal to 2 in equation 1 we get probability at x equal to r is equal to 2 raised to power r into e raised to power minus 2 divided by r factorial r goes from 0, 1, 2, 3 and so on. Therefore probability at x equal to 0 will be equal to 2 raised to power 0 into e raised to power minus 2 divided by 0 factorial that is equal to 1 multiplied by 0.13534 because this is the value of e raised to power minus 2. 2 raised to power 0 will be 1 because anything raised to power 0 is 1, 0 factorial is 1 so this is what we get. And probability at x equal to 4 will be equal to 2 raised to power 4 into e raised to power minus 2 divided by 4 factorial that is equal to 2 into 2 into 2 into e raised to power minus 2 divided by 4 into 3 into 2 into 1. 2 into 2 is 4 so this gets cancelled with 4, 2 with 2 and we are left with 2 by 3 into e raised to power minus 2 that is 2 by 3 into 0.13534 and this is equal to 0.0902 so probability at x equal to 4 is 0.0902 and probability at x equal to 0 is 0.13534. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.