Discrete Mathematics

Continuous Random Variables

Continuous Random Variables - Cumulative Distribution Function

         

If the cumulative distribution function of a continuous random variable XX is F(x)={0(x<0)150x2(0x<5)150x2+25x1(5x10)1(x>10)F(x)=\begin{cases}0\qquad&(x<0)\\ \frac{1}{50}x^2\qquad&(0\leq x<5)\\ -\frac{1}{50}x^2+\frac{2}{5}x-1\qquad&(5\leq x\leq10)\\ 1\qquad&(x>10) \end{cases} what is P(4X6)?P(4\leq X\leq6)?

If the cumulative distribution function of a continuous random variable XX is F(x)=ax (0x9),F(x)=ax~(0\leq x\leq 9), what is P(1X5)?P(1\leq X\leq5)?

Which of the following represents the graph of the cumulative distribution function of a continuous random variable?

(A)

(B)

(C)

(D)

If the cumulative distribution function of a continuous random variable XX is F(x)=ax3 (3<x5),F(x)=a\sqrt{x-3}~(3<x\leq 5), which of the following represents the probability density function f(x)?f(x)?

If the probability density function of a continuous random variable XX is f(x)=ax+1 (0x4),f(x)=\frac{a}{x+1}~(0\leq x\leq 4), which of the following represents the cumulative distribution function F(x)?F(x)?

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