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3 years ago

I need help Knowing What This thing does Before they ban me XD meme life

Mathematics

1 answer:

ElenaW [278]3 years ago

8 0

Helps I get answers when u need help with school mark brainliest and memes for life

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The n candidates for a job have been ranked 1, 2, 3,..., n. Let X 5 the rank of a randomly selected candidate, so that X has pmf

jeka57 [31]

Question:

The n candidates for a job have been ranked 1, 2, 3,..., n. Let x = rank of a randomly selected candidate, so that x has pmf:

$p(x) = \left \{ {{\frac{1}{n}\ \ x=1,2,3...,n} \atop {0\ \ \ Otherwise}} \right.$

(this is called the discrete uniform distribution).

Compute E(X) and V(X) using the shortcut formula.

[Hint: The sum of the first n positive integers is $\frac{n(n +1)}{2}$ , whereas the sum of their squares is $\frac{n(n +1)(2n+1)}{6}$

Answer:

$E(x) = \frac{n+1}{2}$

$Var(x) = \frac{n^2 -1}{12}$ or $Var(x) = \frac{(n+1)(n-1)}{12}$

Step-by-step explanation:

Given

PMF

$p(x) = \left \{ {{\frac{1}{n}\ \ x=1,2,3...,n} \atop {0\ \ \ Otherwise}} \right.$

Required

Determine the E(x) and Var(x)

E(x) is calculated as:

$E(x) = \sum \limits^{n}_{i} \ x * p(x)$

This gives:

$E(x) = \sum \limits^{n}_{x=1} \ x * \frac{1}{n}$

$E(x) = \sum \limits^{n}_{x=1} \frac{x}{n}$

$E(x) = \frac{1}{n}\sum \limits^{n}_{x=1} x$

From the hint given:

$\sum \limits^{n}_{x=1} x =\frac{n(n +1)}{2}$

So:

$E(x) = \frac{1}{n} * \frac{n(n+1)}{2}$

$E(x) = \frac{n+1}{2}$

Var(x) is calculated as:

$Var(x) = E(x^2) - (E(x))^2$

Calculating: $E(x^2)$

$E(x^2) = \sum \limits^{n}_{x=1} \ x^2 * \frac{1}{n}$

$E(x^2) = \frac{1}{n}\sum \limits^{n}_{x=1} \ x^2$

Using the hint given:

$\sum \limits^{n}_{x=1} \ x^2 = \frac{n(n +1)(2n+1)}{6}$

So:

$E(x^2) = \frac{1}{n} * \frac{n(n +1)(2n+1)}{6}$

$E(x^2) = \frac{(n +1)(2n+1)}{6}$

So:

$Var(x) = E(x^2) - (E(x))^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - (\frac{n+1}{2})^2$

$Var(x) = \frac{(n+1)(2n+1)}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +n+2n+1}{6} - \frac{n^2+2n+1}{4}$

$Var(x) = \frac{2n^2 +3n+1}{6} - \frac{n^2+2n+1}{4}$

Take LCM

$Var(x) = \frac{4n^2 +6n+2 - 3n^2 - 6n - 3}{12}$

$Var(x) = \frac{4n^2 - 3n^2+6n- 6n +2 - 3}{12}$

$Var(x) = \frac{n^2 -1}{12}$

Apply difference of two squares

$Var(x) = \frac{(n+1)(n-1)}{12}$

3 0

3 years ago

suppose that prices of a certain model of new homes are normally distributed with a mean of $150000. Use the 68-95-99.7 rule to

Svetllana [295]

Using the Empirical Rule, it is found that 49.85% of buyers paid between $150,000 and $154,800.

<h3>What does the Empirical Rule state?</h3>

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Considering the given mean and standard deviation, the interval between $150,000 and $154,800 corresponds to the interval between the mean and 3 standard deviations above the mean.

The normal distribution is symmetric(50% above the mean, 50% below), hence the percentage corresponding to this interval is:

P = 0.5 x 99.7% = 49.85%.

More can be learned about the Empirical Rule at brainly.com/question/24537145

#SPJ1

5 0

2 years ago

Let f(x)= 3x-2 and g(x)=4x+1<br><br> Find (fog)(x)<br><br> Please help!!!

Lisa [10]

Answer:

f(g(x)) = 12x + 1

Step-by-step explanation:

Step 1: Define functions

f(x) = 3x - 2

g(x) = 4x + 1

Step 2: Find f(g(x))

f(g(x)) = 3(4x + 1) - 2

f(g(x)) = 12x + 3 - 2

f(g(x)) = 12x + 1

3 0

4 years ago

-2(v- 2) =-3 -22<br> What’s the answer?

Mumz [18]

Answer:

v= 29/2

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

−2(v−2)=−3−22

(−2)(v)+(−2)(−2)=−3+−22(Distribute)

−2v+4=−3+−22

−2v+4=(−3+−22)(Combine Like Terms)

−2v+4=−25

Step 2: Subtract 4 from both sides.

−2v+4−4=−25−4

−2v=−29

Step 3: Divide both sides by -2.

−2v

−2

−29

−2

29/2

5 0

3 years ago

Read 2 more answers

Adding and Subtracting Polynomials

wolverine [178]

Answer:

Step-by-step explanation:

8 0

3 years ago