Sum

The p.d.f. of a continuous r.v. X is

f(x) = `{((3x^2)/(8), "for" 0 < x < 2),(0, "otherwise".):}`

Determine the c.d.f. of X and hence find P(X < –2)

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#### Solution

F(x) = `int_0^x(x)*dx`

= `int_0^x (3x^2)/(8)*dx`

= `(3)/(8) int_0^x x^2*dx`

= `(1)/(8)[x^3]_0^x`

= `x^3/(8)`

P(X < –2)

= F(–2)

= 0 ...`[("f"(x) = 0 "if" x ∉ (0.2)),(therefore "F"(x) = 1 "for" x ≤ 0)]`

Is there an error in this question or solution?

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