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2 Statistics

The random variable $X\,$ has the distribution $X∼B(6,0.35)X\sim B(6,0.35)$ .

One term in the expansion of $0.65+0.35)^6$ is $(62)(0.65)4(0.35)2\binom62(0.65)^4(0.35)^2$ .

State the probability involving $X\,$ that this term represents.

[1]

Explain why the sum of all seven terms in the expansion is equal to the sum of the probabilities $P (X = r)$ for $r=0,1,…,6r=0,1,\ldots,6$ .

[2]

2 Statistics Questions

The random variable $X\,$ has the distribution $X∼B(6,0.35)X\sim B(6,0.35)$ .

One term in the expansion of $0.65+0.35)^6$ is $(62)(0.65)4(0.35)2\binom62(0.65)^4(0.35)^2$ .

State the probability involving $X\,$ that this term represents.

[1]

Explain why the sum of all seven terms in the expansion is equal to the sum of the probabilities $P (X = r)$ for $r=0,1,…,6r=0,1,\ldots,6$ .

[2]