Brilliant

Home Courses Today

Excel in math and science.

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Your answer seems reasonable. Find out if you're right!

That seems reasonable. Find out if you're right!

Join using Facebook Join using Google Join using email

Forgot password? New user? Sign up

Existing user? Log in

Probability

Continuous Random Variables

Concept Quizzes

Continuous Random Variables - Probability Density Function (PDF)
Continuous Random Variables - Cumulative Distribution Function
Higher Moments Warmup
Continuous Random Variables - Joint Probability Distribution
Continuous Random Variables - Problem Solving

Continuous Random Variables - Probability Density Function (PDF)

If the probability density function of a continuous random variable $X\in[-1,7]$ is given by $f(x)=a(x+1)(x-7),$ what is $P(0\le X\le4)?$

\frac{4}{5}

\frac{41}{64}

\frac{13}{64}

\frac{13}{32}

Show explanation

View wiki

by Brilliant Staff

The probability density function of a continuous random variable $X$ that ranges from 1 to $e^{2}$ is given by $f(x)=\frac{1}{2x}.$ Find the value of $k$ such that $P(X>k)=\frac{1}{10}.$

\ln{\frac{9}{5}}

e^{\frac{9}{5}}

1+\ln{\frac{5}{9}}

1+e^{\frac{5}{9}}

Show explanation

View wiki

by Brilliant Staff

If the probability density function of a continuous random variable $X$ is given by $f(x)=\begin{cases} ax^2\ &(0\le x\le1) \\-\frac{a}{9}(x-1)+a\ &(1<x\le10),\end{cases}$ what is the value of $a?$

\frac{6}{29}

\frac{3}{31}

\frac{3}{29}

\frac{6}{31}

Show explanation

View wiki

by Brilliant Staff

If the probability density function of a continuous random variable $X\in[0,\frac{\pi}{16}]$ is given by $f(x)=a\sin8x,$ what is the variance of $X$ divided by $\pi-3 ?$

\frac{1}{32}

\frac{1}{64}

\frac{1}{8}

\frac{1}{4}

Show explanation

View wiki

by Brilliant Staff

If the probability density function of a continuous random variable $X$ is given by $f(x)=11x^{10}\ (0\le x\le1),$ what is $E[X]?$

\frac{10}{11}

\frac{11}{12}

\frac{12}{11}

\frac{11}{10}

Show explanation

View wiki

by Brilliant Staff

Problem Loading...

Note Loading...

Set Loading...