Recent questions tagged gravner

Each day, you independently decide, with probability p, to flip a fair coin. Otherwise, you do nothing. (a) What is the probability of getting exactly 10 Heads in the fir...

Roll a die $n$ times and let $M$ be the number of times you roll $6$. Assume that $n$ is large.(b) Write down an approximation, in terms on $n$ and $\phi$, of the probabi...

After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...

After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...

After your complaint about their service, a representative of an insurance company promised to call you "between $7$ and $9$ this evening." Assume that this means that th...

A random variable $X$ has the density function$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$(c) Determine the probability density ...

A random variable $X$ has the density function$f(x)= \begin{Bmatrix} c(x+\sqrt{x}) & x\epsilon [0,1]\\ 0& otherwise \end{Bmatrix}.$(a) Determine c.

How many times do you need to toss a fair coin to get $100$ heads with probability $90$%?

Assume that $X$ is Normal with mean $\mu$ $=$ $2$ and variance $\sigma^2$ $=$ $25$. Compute the probability that $X$ is between $1$ and $4$.

What is the probability that a Normal random variable differs from its mean $\mu$ by more than 3 $\sigma$ ?

What is the probability that a Normal random variable differs from its mean $\mu$ by more than 2 $\sigma$ ?

What is the probability that a Normal random variable differs from its mean $\mu$ by more than $\sigma$ ?

Let X be a $N(\mu , \sigma^2)$ random variable and let $Y = \alpha X+\beta$, with $\alpha$ $0$. How is $Y$ distributed?

$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(c) Determine EX and Var(X).

$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(b) Compute $P(1\leqslant X\leqslant 2)$

$f(x) = \begin{Bmatrix} cx & if (0<x<4) \\ 0 & otherwise \end{Bmatrix}$(a) Determine $c$.