00:01
Given in the questions that for independent rules of this excited life, so we ask let x is equal to 25 and y is equal to 35.
00:13
Now we have to obtain joint pmf of x in 1.
00:17
So probability of getting a probability of 1 is equal to 1 over 6.
00:24
Similarly, probability of getting 2 is equal to 1 over 6.
00:30
So joint pmf of x and i is as follows.
00:35
Joint probability mass function pma, x and y can we do to us.
00:43
P of x is equal to x, comma, y is equal to y to c quality.
00:48
Y factorial over x factorial times x, y, factorialial times of y minus x minus y factorialial into y 6xxxxx par x, y, 6xxxxxxxxx paris, x times times 1 over 6 power x times 1 over 6 power 1 times 4 over 6 power 1.
01:19
So we have p of x is equal to 0 comma y is equal to 0 2 x squared way divided 0 factorial times x factorial x times 0 factorial x times 4 minus 0 times 1 over 6 power 0 times 1 over 6 power 0 times 4 minus 0 minus 0.
01:45
This will be equal to 4 factorial over x factorial times of 4 factorial might apply by 1 times of 1 times 4 over 6 power 4.
02:00
So i'm calculating this we get the required probability of x equal to 0 comma y is equal to 0 will be equal to 0 .1975.
02:12
Now next on calculating the of x is equal to 1 comma y is equal to 0 we have 4 factor divided by 1 factorial times of 0 factorial times 4 minus 1 minus 0 multiplied by 1 over 6 power 1 1 over 6 power 0 and 4 over 6 power 0 4 minus 1.
02:38
Therefore, we have 4 factorial divided by 1 times of 0 times 3 factorial times with 1 over 6 power 1, 1 over 6 power 0, multiplied by 4 over 6 power 3...