Denote by $R,K$ the random variables representing the integer values $r,k$ , respectively. Then $R\sim\mathrm{Unif}(-2,5)$ and $K\sim\mathrm{Unif}(2,7)$ , where $\mathrm{Unif}(a,b)$ denotes the discrete uniform distribution over the interval $[a,b]$ . So $R$ and $K$ have probability mass functions

$p_R(r)=\begin{cases}\dfrac18&\text{for }r\in\{-2,-1,\ldots,5\}\\\\0&\text{otherwise}\end{cases}$

$p_K(k)=\begin{cases}\dfrac16&\text{for }k\in\{2,3,\ldots7\}\\\\0&\text{otherwise}\end{cases}$

We want to find $P\left(\dfrac RK\equiv0\pmod n\right)$ , where $n$ is any integer.

We have six possible choices for $K$ :

(i) if $K=2$ , then $\dfrac RK$ is an integer when $R=\pm2,0,4$ ;

(ii) if $K=3$ , then $\dfrac RK$ is an integer when $R=0,3$ ;

(iii) if $K=4$ , then $\dfrac RK$ is an integer when $R=0,4$ ;

(iv) if $K=5$ , then $\dfrac RK$ is an integer when $R=0,5$ ;

(v) if $K=6$ or $K=7$ , then $\dfrac RK$ is an integer only when $R=0$ in both cases.

If the selection of $R,K$ are made independently, then the joint distribution is the product of the marginal distribution, i.e.

$p_{R,K}(r,k)=p_R(r)\cdot p_K(k)=\begin{cases}\dfrac1{48}&\text{for }(r,k)\in[-2,5]\times[2,7]\\\\0&\text{otherwise}\end{cases}$

That is, there are 48 possible events in the sample space. We counted 12 possible outcomes in which $\dfrac RK$ is an integer, so the probability of this happening is $\dfrac{12}{48}=\dfrac14$ .

7 0

3 years ago

Help will name Brainliest

11111nata11111 [884]

Answer:

x = $\frac{\sqrt{22} }{2}$

Step-by-step explanation:

Using the Pythagorean Theorem we can solve this problem.

The legs of the triangle will be the same (the dashes in the middle of the line indicates they are the same).

The Pythagorean Theorem will look like this:

$a^{2}+a^{2} = (\sqrt {11})^{2}$

Now, let's find a:

$2a^{2} = 11$ The square of a radical will be whatever is under the arch

$a^{2}=\frac{11}{2}$ Divide 11 by 2

$\sqrt{a^{2} } = \sqrt{\frac{11}{2} }$ Square root both sides

a = $\frac{\sqrt{22} }{2}$

Therefore, the length of side x is equal to $\frac{\sqrt{22} }{2}$ .

Hope this helps!!

8 0

2 years ago

For the data set below, calculate the standard deviation to the nearest hundredth decimal place. 27 38 47 42 33 56 37 57 38 52

mihalych1998 [28]

In order to calculate standard deviation, apply the standard deviation formula, which is given in the attached file. In this formula, we are finding the square root of the sum of the square of given values less their mean value (the sum of the given numbers divided to their amount) divided to N-1, where N is the amount of the given numbers. When we calculate the mean, it is 42.7 and the standard deviation is 10.02275

5 0

4 years ago

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