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3 years ago

Question 1 (1 point)

Mathematics

1 answer:

Leni [432]3 years ago

6 0

<h3> $▪▪▪▪▪▪▪▪▪▪▪▪▪ {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪$ </h3><h3 /><h3><u>Question</u> 1 </h3>

Money spent semi - annually (in 6 months) = $ 150

So, money spent annually (12 months) is equal to :

$150 \times 2$

$\$ \: 300$

<h3><u>Question</u> 2</h3>

Her budget annually (in 12 months) = $ 900

So, budget monthly is equal to :

$\dfrac{900}{12}$

$\$ \: 75$

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3 years ago

Xander spends most of his time with his 10 closest friends. he has known 4 of his 10 friends since kindergarten. if he is going

Mademuasel [1]

Probability that the first 2 of the friends to show up to the movie are friends he has known since kindergarten but the third not is 1/10

Total friends = 10

Friends from kindergarten = 4

Probability is the chance that a given event will occur. Probability of an event lies within 0 to 1

P(E) = Favourable outcomes / Total outcomes

Probability of getting 1st friend from kindergarten = 4/10

Probability of getting 2nd friend from kindergarten = 3/9

Probability of getting 3rd friend not from kindergarten = 6/8

Since all these probabilities are independent, We can use Multiplicative identity. Thus,

Required probability is 4/10 * 3/9 * 6/8

= 1/10

Thus, Probability that the first 2 of the friends to show up to the movie are friends he has known since kindergarten but the third not is 1/10

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brainly.com/question/7514534

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2 years ago

Square of a standard normal: Warmup 1.0 point possible (graded, results hidden) What is the mean ????[????2] and variance ??????

LenaWriter [7]

Answer:

$E[X^2]= \frac{2!}{2^1 1!}= 1$

$Var(X^2)= 3-(1)^2 =2$

Step-by-step explanation:

For this case we can use the moment generating function for the normal model given by:

$\phi(t) = E[e^{tX}]$

And this function is very useful when the distribution analyzed have exponentials and we can write the generating moment function can be write like this:

$\phi(t) = C \int_{R} e^{tx} e^{-\frac{x^2}{2}} dx = C \int_R e^{-\frac{x^2}{2} +tx} dx = e^{\frac{t^2}{2}} C \int_R e^{-\frac{(x-t)^2}{2}}dx$

And we have that the moment generating function can be write like this:

$\phi(t) = e^{\frac{t^2}{2}$

And we can write this as an infinite series like this:

$\phi(t)= 1 +(\frac{t^2}{2})+\frac{1}{2} (\frac{t^2}{2})^2 +....+\frac{1}{k!}(\frac{t^2}{2})^k+ ...$

And since this series converges absolutely for all the possible values of tX as converges the series e^2, we can use this to write this expression:

$E[e^{tX}]= E[1+ tX +\frac{1}{2} (tX)^2 +....+\frac{1}{n!}(tX)^n +....]$

$E[e^{tX}]= 1+ E[X]t +\frac{1}{2}E[X^2]t^2 +....+\frac{1}{n1}E[X^n] t^n+...$

and we can use the property that the convergent power series can be equal only if they are equal term by term and then we have:

$\frac{1}{(2k)!} E[X^{2k}] t^{2k}=\frac{1}{k!} (\frac{t^2}{2})^k =\frac{1}{2^k k!} t^{2k}$

And then we have this:

$E[X^{2k}]=\frac{(2k)!}{2^k k!}, k=0,1,2,...$

And then we can find the $E[X^2]$

$E[X^2]= \frac{2!}{2^1 1!}= 1$

And we can find the variance like this :

$Var(X^2) = E[X^4]-[E(X^2)]^2$

And first we find:

$E[X^4]= \frac{4!}{2^2 2!}= 3$

And then the variance is given by:

$Var(X^2)= 3-(1)^2 =2$

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3 years ago

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