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Discrete Mathematics

# Continuous Random Variables - Cumulative Distribution Function

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

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

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 $$X$$ is $F(x)=a\sqrt{x-3}~(3<x\leq 5),$ which of the following represents the probability density function $$f(x)?$$

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

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