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Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 1.2 - Problem 12e
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 1.2 - Problem 12e

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# Prove Hint: Consider (1 ? 1)n and (1 + 1)n, or use

ISBN: 9780321923271 41

## Solution for problem 12E Chapter 1.2

Probability and Statistical Inference | 9th Edition

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Problem 12E

PROBLEM 12E

Prove

Hint: Consider (1 − 1)n and (1 + 1)n, or use Pascal’s equation and proof by induction.

Step-by-Step Solution:
Step 1 of 3

Solution 12E

Step1 of 3:

We need to prove,

nCr =0  and  =

Consider (1 − 1)n and (1 + 1)n, or use Pascal’s equation and proof by induction.

Step2 of 3:

Consider,

nCr = 0

Proof: we know that the pascal’s equation is given by

nCr

Substitute a = -1 and b = 1 in above equation we get

nCr

= nCr

0 = nCr

0 = nCr{}

0 = nCr{}

0 = nCr

Therefore, nCr = 0

Hence the proof.

Step2 of 3:

Again consider,

=

Proof: we know that the pascal’s equation is given by

nCr

Substitute a = 1 and b = 1 in above equation we get

nCr

= nCr

= nCr

= nCr{}

= nCr{}

= nCr

Therefore, nCr =

Hence the proof.

Step 2 of 3

Step 3 of 3

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