You have $40.50 to spend for a pair of jeans. The sales tax is 6%. What is the most the jeans can cost?

A random variable X with a probability density function () = {^-x > 0

Sliva [168]

The solutions to the questions are

The probability that X is between 2 and 4 is 0.314
The probability that X exceeds 3 is 0.199
The expected value of X is 2
The variance of X is 2

<h3>Find the probability that X is between 2 and 4</h3>

The probability density function is given as:

f(x)= xe^ -x for x>0

The probability is represented as:

$P(x) = \int\limits^a_b {f(x) \, dx$

So, we have:

$P(2 < x < 4) = \int\limits^4_2 {xe^{-x} \, dx$

Using an integral calculator, we have:

$P(2 < x < 4) =-(x + 1)e^{-x} |\limits^4_2$

Expand the expression

$P(2 < x < 4) =-(4 + 1)e^{-4} +(2 + 1)e^{-2}$

Evaluate the expressions

P(2 < x < 4) =-0.092 +0.406

Evaluate the sum

P(2 < x < 4) = 0.314

Hence, the probability that X is between 2 and 4 is 0.314

<h3>Find the probability that the value of X exceeds 3</h3>

This is represented as:

$P(x > 3) = \int\limits^{\infty}_3 {xe^{-x} \, dx$

Using an integral calculator, we have:

$P(x > 3) =-(x + 1)e^{-x} |\limits^{\infty}_3$

Expand the expression

$P(x > 3) =-(\infty + 1)e^{-\infty}+(3+ 1)e^{-3}$

Evaluate the expressions

P(x > 3) =0 + 0.199

Evaluate the sum

P(x > 3) = 0.199

Hence, the probability that X exceeds 3 is 0.199

<h3>Find the expected value of X</h3>

This is calculated as:

$E(x) = \int\limits^a_b {x * f(x) \, dx$

So, we have:

$E(x) = \int\limits^{\infty}_0 {x * xe^{-x} \, dx$

This gives

$E(x) = \int\limits^{\infty}_0 {x^2e^{-x} \, dx$

Using an integral calculator, we have:

$E(x) = -(x^2+2x+2)e^{-x}|\limits^{\infty}_0$

Expand the expression

$E(x) = -(\infty^2+2(\infty)+2)e^{-\infty} +(0^2+2(0)+2)e^{0}$

Evaluate the expressions

E(x) = 0 + 2

Evaluate

E(x) = 2

Hence, the expected value of X is 2

<h3>Find the Variance of X</h3>

This is calculated as:

V(x) = E(x^2) - (E(x))^2

Where:

$E(x^2) = \int\limits^{\infty}_0 {x^2 * xe^{-x} \, dx$

This gives

$E(x^2) = \int\limits^{\infty}_0 {x^3e^{-x} \, dx$

Using an integral calculator, we have:

$E(x^2) = -(x^3+3x^2 +6x+6)e^{-x}|\limits^{\infty}_0$

Expand the expression

$E(x^2) = -((\infty)^3+3(\infty)^2 +6(\infty)+6)e^{-\infty} +((0)^3+3(0)^2 +6(0)+6)e^{0}$

Evaluate the expressions

E(x^2) = -0 + 6

This gives

E(x^2) = 6

Recall that:

V(x) = E(x^2) - (E(x))^2

So, we have:

V(x) = 6 - 2^2

Evaluate

V(x) = 2

Hence, the variance of X is 2

Read more about probability density function at:

brainly.com/question/15318348

#SPJ1

<u>Complete question</u>

A random variable X with a probability density function f(x)= xe^ -x for x>0\\ 0& else

a. Find the probability that X is between 2 and 4

b. Find the probability that the value of X exceeds 3

c. Find the expected value of X

d. Find the Variance of X

7 0

2 years ago

Phil T. Rich has $100 and spends $3 per day. Earnest Worker has only $20 but is adding to it at a

Lelechka [254]

Answer: day 11

equation: 100-3d=20+5e

Step-by-step explanation:

do a table. 100-3: 20+5: 97-3:25+5 until you get to the same number. I think that's how you do it. I hope it helps.

4 0

3 years ago

I also got this one wrong as well can someone tell me what I'm doing wrong so I can change it

Angelina_Jolie [31]

The answer is: [D]: "Subtract 5 from 10" .
____________________________________
Explanation:
____________________________________
Use the correct order of operations, according to the mnemonic:
"PE MD AS".

The "P" stands for "parentheses", which takes top (first priority); and there are values in parentheses in this expression—specifically, the "(10 - 5)" . So the first step is to "subtract 5 from 10" —which is: "Answer choice: [D]".
Your error was starting at the beginning of the problem; and not using the "order of operations".
____________________________________________________

6 0

2 years ago

What is the solution of the inequality below? <br> y-1≥0

irinina [24]

Answer:

y≥1

Step-by-step explanation:

hello :

y-1≥0

y-1+1≥0+1

y≥1

3 0

2 years ago

The frequency distribution shows the lengths, in inches, of available baseball bat at a batting cage. what is the mean of the fr

ivanzaharov [21]

The mean of a frequency distribution is given by
<span>
$\bar{x}= \frac{\Sigma fx}{\Sigma f} \\ \\ = \frac{(27\times2)+(28\times5)+(31\times3)+(33\times1)+(34\times4)}{2+5+3+1+4} \\ \\ = \frac{54+140+93+33+136}{15} = \frac{456}{15} =30.4$ </span>

6 0

3 years ago