Recent questions tagged goclasses-cs-dpp-day-260

How many 15 -letter arrangements of 5 A's, 5 B's, and 5 C's have no A's in the first 5 letters, no B's in the next 5 letters, and no C's in the last 5 letters?$\sum_{k=0}...

A large equilateral triangle is constructed by using toothpicks to create rows of small equilateral triangles. For example, in the figure, we have 3 rows of small congrue...

Pat is to select six cookies from a tray containing only chocolate chip, oatmeal, and peanut butter cookies. There are at least six of each of these three kinds of cookie...

Let the set $\mathcal{S}=\{8,5,1,13,34,3,21,2\}$. Susan makes a list as follows: for each two-element subset of $\mathcal{S}$, she writes on her list the greater of the s...

How many three-digit numbers have at least one 2 and at least one 3 ?52545658

Suppose that $X$ and $Y$ are independent random variables, such that :$P(X=x)=\frac{1}{4}\left(\frac{3}{4}\right)^{x-1}$ for integers $x\ge 1$, and $P(Y=y)=\frac{1}{2}\le...

Let $X_1,X_2,\ldots,X_n$ be independent discrete uniform random variables on ${1,2,\ldots,n}$. That is, $P(X_i=j)=\frac{1}{n}$ for each $i$ and each $j\in{1,2,\ldots,n}$....

Suppose that $X$, $Y$, and $Z$ are independent random variables such that : $P(X=x)=\frac{1}{2}\left(\frac{1}{2}\right)^{x-1}$ for integers $x\ge 1$,  $P(Y=y)=\frac{1}{3}...

Let $X_1,X_2,X_3$ be independent continuous uniform random variables on $[0,1]$. Let $k\in[0,1]$ be a constant. Find $P(\max(X_1,X_2,X_3)>k)$.$1-k$ $1-k^2$ $1-k^3$ $(1-k)...

Let $X$ be a random variable with PDF :$$f(x)= \begin{cases}C x^2(1-x)^3 & 0 <x<1\\\\ 0 & \text{otherwise} \end{cases}$$What is $C$?