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3 years ago

PLS HELP ME ON THIS PLSSSS

Mathematics

1 answer:

Deffense [45]3 years ago

5 0

Answer:

Step-by-step explanation:

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Consider a discrete random variable x with pmf px (1) = c 3 ; px (2) = c 6 ; px (5) = c 3 and 0 otherwise, where c is a positive

PtichkaEL [24]

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,

$\mathbb P(X>2)=\mathbb P(X=5)=\dfrac c3=\dfrac25$

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

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

If $Y=X^2+1$ , then $X^2=Y-1\implies X=\sqrt{Y-1}$ , where we take the positive root because we know $X$ can only take on positive values, namely 1, 2, and 5. Correspondingly, we know that $Y$ can take on the values $1^2+1=2$ , $2^2+1=5$ , and $5^2+1=26$ . At these values of $Y$ , we would have the same probability as we did for the respective value of $X$ . 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.

8 0

3 years ago

Apples come in bags of 4. Oranges come in bags of 6.

muminat

Answer: Apples come in bags of 4. Oranges come in bags of 6.

so it going to be Multiple 4x6=24 I explain it, is this how you want it

Step-by-step explanation: hope this help

3 0

3 years ago

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Algebra 2 help please

Andre45 [30]

(gof)(x) = g(f(x))

so

g(f(x)) = 3(6x - 4)^2 -2(6x - 4) - 10
g(f(x)) = 3(36x^2 - 48x + 16) - 12x + 8 - 10
g(f(x)) = 72x^2 - 144x + 48 - 12x - 2
g(f(x)) = 72x^2 - 156x + 46

answer
(gof)(x) = 72x^2 - 156x + 46

4 0

3 years ago

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Estimate:________<br>74,529<br>- 38453

kiruha [24]

Answer:

35,000?

Step-by-step explanation:

3 0

3 years ago

2 divided by 3 5/8 PLease help I really need it

trasher [3.6K]

Answer:

16/29

Step-by-step explanation:

2 ÷ 3 5/8

= 2 ÷ 29/8

= 2/1 × 8/29

= 2 × 8/ 1 × 29

= 16/29

Hope it helps!

8 0

1 year ago

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