The discrete random variable Y has probability...

The discrete random variable Y has probability distribution y | 1 | 2 | 3 | 4 P(Y=y) | a | b | 0.3 | c where a, b and c are constants. The cumulative distribution function F(y) of Y is given in the following table y | 1 | 2 | 3 | 4 F(y) | 0.1 | 0.5 | d | 1.0 where d is a constant. (a) Find the value of a, the value of b, the value of c and the value of d. (b) Find P(3Y + 2 ? 8).

Transcript

00:01 Hi, i'm david and i'm here to have you answer your question.

00:04 Now let me bring up your question here.

00:07 Let me make it small here.

00:11 Now in this question we're given the discrete random variable y probability distribution and the community distribution as well.

00:19 Now let me remind you that for the probability distribution, the sum of the probability equal to small y must equal to 1.

00:29 And f y here it just equal to the proper pt x is proper pt w smaller equal to the y and now we are given the table but missing some value and then the apc and d here now to find the first one a we notice that the value 0 .1 it will be the proper ptium x smaller equal to 1 and because why it's starting from the value 1 therefore this one will be the same as the a so our a here we know that a equal to 0 1 that will be the first thing we see now for the value 0 .5 it will be the proper pt x smaller equal to 2 proper pt x small equal to 2 means that it would equal to proper pt x equal to 1 plus the proper pt x to 2 and equal to 0 .5.

01:36 We know x x equals 1 equal to 1 equal to 0 .1 already, plus this one we don't know equal to 0 .5.

01:46 Therefore probability x equals 2, this only changed equal to p, it will equal to 0 .5 minus 0 .1, so equal to 0 .4.

01:56 Therefore we found that that p equal to 0 .4.

02:00 Now to find the d, we know that and the value here means that probability of the x equal to 3, equal to 3, and d is equal to the probability x small equal to 3.

02:18 It will equal to the property x small equals 2 plus property x equal to 3.

02:25 Therefore, probability x.

02:28 Equal to 2 we 5, the property xx2 will equal to the 0 .3...

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