If x is a binomial random variable, compute P(x) for each of...

If \(x\) is a binomial random variable, compute \(P(x)\) for each of the following cases: (a) \(P(x \le 1)\), \(n = 4\), \(p = 0.8\) \(P(x) =\) (b) \(P(x > 2)\), \(n = 3\), \(p = 0.7\) \(P(x) =\) (c) \(P(x < 2)\), \(n = 7\), \(p = 0.7\) \(P(x) =\) (d) \(P(x \ge 2)\), \(n = 3\), \(p = 0.1\) \(P(x) =\)

Transcript

00:01 In this question, they given the binomial random variable.

00:05 So for that, we have to find out the compute the p of x for each of the following cases.

00:11 So they given the four cases here, we have to compute the polynomial of p of x for each case.

00:19 So let come to the first case here.

00:22 So in this, the n is equal to 8 and p is equal to 0 .2.

00:27 So for this, the p of x is equal to x here.

00:34 That is equal to 8x.

00:38 So multiply by 0 .2 whole power x, multiply by 1 minus 0 .2 whole power 8 minus x here.

00:48 So x values are 0 comma 1, 2 comma, and so on 8, up to 8.

00:55 So that is equal to here 8 x.

00:59 So multiply by 0 .2x.

01:03 So here multiply by 0 .8 whole power 8 minus x.

01:09 So in this p of x less than r equal to 6 here, that is equal to here.

01:21 P of x is equal to 0 plus p of x is equal to 1 plus p of x is equal to 1 plus p of of x is equal to 2 and place p of x is equal to 3 plus p of x is equal to 4 place here p of x is equal to 5 so up to p of x is equal to 6 here so now that is equal to here 1 minus p of x is equal to 7 that is equal to 1 minus p of x greater than are equal to 7 here so that is equal to 1 minus here p of x greater than at equal to 7 is equal to here 8 so x value is 7 here that is 7 multiply by here 0 .2 whole power 7 and here 0 .8 whole power 1 so after substituting the x value is equal to 7 we get this one and finally from this that is equal to here so 1 minus this value is to 0 point so double 0 again double 0171 so therefore from this information p of x less than are equal to 6 is equal to get the value 0 .99 so 99 here so this is the final answer to the first case now let come to the second case here so in second one so that is b so in this n is equal to 3 comma p is equal to 0 .2, that is p of x is equal to x here, that is equal to here 3x...

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