Mathematics: PLS HURR Which word describes the 5 in the expression 5n? A. coefficient B. exponent C. product D. sum

Looks like the PMF is supposed to bewhich is kinda weird, but it s not entirely clear what you meant...Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:Next,If , then , where we take the positive root because we know can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that can take on the values , , and . At these values of , we would have the same probability as we did for the respective value of . That is,Part...

PLS HURR Which word describes the 5 in the expression

Ответ:

blessing03

24.05.2021

Mathematics

Step-by-step explanation:

It would be either A or C

Most likely A Hope this helps ya <3

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Ответ:

030702princessjs

19.08.2022

Mathematics

Looks like the PMF is supposed to be

$\mathbb P(X=x)=\begin{cases}\dfrac c3&\text{for }x\in\{1,5\}\\\\\dfrac c6&\text{for }x=2\\\\0&\text{otherwise}\end{cases}$

which is kinda weird, but it's not entirely clear what you meant...

Anyway, assuming the PMF above, for this to be a valid PMF, we need the probabilities of all events to sum to 1:

$\displaystyle\sum_{x\in\{1,2,5\}}\mathbb P(X=x)=\dfrac c3+\dfrac c6+\dfrac c3=\dfrac{5c}6=1\implies c=\dfrac65$

Next,

$\mathbb P(X2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

$\mathbb E(X)=\displaystyle\sum_{x\in\{1,2,5\}}x\,\mathbb P(X=x)=\dfrac c3+\dfrac{2c}6+\dfrac{5c}3=\dfrac{7c}3=\dfrac{14}5$

$\mathbb V(X)=\mathbb E\bigg((X-\mathbb E(X))^2\bigg)=\mathbb E(X^2)-\mathbb E(X)^2$
$\mathbb E(X^2)=\displaystyle\sum_{x\in\{1,2,5\}}x^2\,\mathbb P(X=x)=\dfrac c3+\dfrac{4c}6+\dfrac{25c}3=\dfrac{28c}3=\dfrac{56}5$
$\implies\mathbb V(X)=\dfrac{56}5-\left(\dfrac{14}5\right)^2=\dfrac{84}{25}$

If Y=X^2+1

, then $X^2=Y-1\implies X=\sqrt{Y-1}$ , where we take the positive root because we know

can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that

can take on the values 1^2+1=2

, and

. At these values of

, we would have the same probability as we did for the respective value of

. That is,

$\mathbb P(Y=y)=\begin{cases}\dfrac c3&\text{for }y=2\\\\\dfrac c6&\text{for }y=5\\\\\dfrac c3&\text{for }y=26\\\\0&\text{otherwise}\end{cases}$

Part (5) is incomplete, so I'll stop here.

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PLS HURR Which word describes the 5 in the expression 5n? A. coefficient B. exponent C. product D. sum

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