Continuous Random Variables

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 $P(4\leq X\leq6)?$

\frac{11}{25}

\frac{9}{50}

\frac{11}{50}

\frac{9}{25}

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

\frac{5}{18}

\frac{4}{9}

\frac{5}{9}

\frac{2}{9}

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

(A)

(B)

(C)

(D)

(A)

(B)

(C)

(D)

If the cumulative distribution function of a continuous random variable $X$ is $F(x)=a\sqrt{x-3}~(3$ which of the following represents the probability density function $f(x)?$

f(x)=\frac{1}{2\sqrt{3(x-3)}}

f(x)=\frac{2}{3\sqrt{2}}(x-3)\sqrt{x-3}

f(x)=\frac{2}{3\sqrt{3}}(x-3)\sqrt{x-3}

f(x)=\frac{1}{2\sqrt{2(x-3)}}

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 $F(x)?$

F(x)=\log_{4}x

F(x)=\frac{1}{4}x

F(x)=\log_{5}(x+1)

F(x)=\frac{5}{(x+1)^2}

Concept Quizzes

Continuous Random Variables - Cumulative Distribution Function