*4.10. Prove: (a) T = N ×B = -B ×N; (b) N = B ×T = -T...

Transcript

00:01 In this question, the motive is to prove that the binomial probability mass function which is here x then it will be n, p is equals to the probability mass function where we are having n minus x and then it is n, 1 minus p.

00:20 So let's see how we can prove this expression and here we can write that binomial probability mass function which is here as such.

00:30 So this will be equals to ncx or we can simply write it nx and now it is p raised to the power x 1 minus p raised to the power n minus x.

00:44 So in this very expression we need to apply two different operations.

00:48 So this is the lhs value, right? lhs means left hand side expression.

00:54 So here we need to substitute, let's write it is x with n minus x.

01:01 So let's write over here x with and now it is going to be here n minus x and the second operation is to replace.

01:11 So we need to replace the value of p with 1 minus p.

01:16 So from this two operation our above expression can be here rewritten as the probability mass function of n minus x.

01:27 Here also we need to replace right and then it will be n now it is comma 1 minus p.

01:35 So this is equals to n now here it will be n minus x.

01:41 And then it is 1 minus p raised to the power n minus x and then it will be p raised to the power n minus it is n minus x and if we simplify this very expression then it is here going to be equals to n.

02:00 Now it will be n minus x and here it is 1 minus p raised to the power n minus x and then it is p raised to the power x...

Question

*4.10. Prove: (a) T = N \times B = -B \times N; (b) N = B \times T = -T \times B; (c) B = T \times N = -N \times T.

Question

*4.10. Prove: (a) T = N \times B = -B \times N; (b) N = B \times T = -T \times B; (c) B = T \times N = -N \times T.

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