#statistics problem

Probability 2

Let the random variables X follow B (6, p) If 16;P;( X = 4 ) = P;( X = 2 ) , then what is the value of p

Look at it this way: solving fully: apply relevant formula, put numbers, compute. Result comes as 1/5. Easy verification shows it satisfies condition.

Ref: NCERT Mathematics Class XII — Probability

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General Mathematics 2

The values of c for which the function f(x) is a p.d.f. is? f( x ) = array*20c c x ,&0 < x < 4 0,&otherwise array .

Understanding this is easy: using formula we get 1/4. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 1/4.

Ref: NCERT Mathematics Class XI and XII

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Probability 2

Find the mean of the Binomial distribution if n = 10, p = 4/5, q = 1/5

Look at it this way: we verify 8 by full calculation: use standard identity, substitute, simplify step by step to reach 8.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

In a binomial distribution, the mean is 4 and variance is 3. Then the mode is

In easy words, np=4, npq=3 gives q=0.75,p=0.25,n=16. Mode=floor((n+1)p)=floor(4.25)=4. Complete.

Ref: NCERT Mathematics Class XII — Probability

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