#probability density function

Probability 2

The random variable X has a probability density function as given by f( x ) = array*20c 3x^2,;;0 x 1 0,;;otherwise array

Applying the basic concept, using formula we get 3/5. Calculation gives this directly, check steps: apply rule, substitute values, simplify to get 3/5.

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

The random variable X has probability density function as given by f( x ) = array*20c 3x^2,;;0 x 1 0,;;otherwise array .

From the definition, after simplifying, 0.6 is left. The method is simple: formula → substitution → calculation → answer.

Ref: NCERT Mathematics Class XII — Probability

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Probability 1

The value of k for which the function f( x ) = array*20c ke^ - 3x,&x > 0 0&elsewhere array . is probability density func

Look at it this way: we verify 3 by full calculation: use standard identity, substitute, simplify step by step to reach 3.

Ref: NCERT Mathematics Class XII — Probability

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