Hi need help for this maths question

Answers

Answer 1

a) If f(y) is a probability density function, then both f(y) ≥ 0 for all y in its support, and the integral of f(y) over its entire support should be 1. eˣ > 0 for all real x, so the first condition is met. We have

[tex]\displaystyle \int_{-\infty}^\infty f(y) \, dy = \frac14 \int_0^\infty e^{-\frac y4} \, dy = -\left(\lim_{y\to\infty}e^{-\frac y4} - e^0\right) = \boxed{1}[/tex]

so both conditions are met and f(y) is indeed a PDF.

b) The probability P(Y > 4) is given by the integral,

[tex]\displaystyle \int_{-\infty}^4 f(y) \, dy = \frac14 \int_0^4 e^{-\frac y4} \, dy = -\left(e^{-1} - e^0\right) = \frac{e - 1}{e} \approx \boxed{0.632}[/tex]

c) The mean is given by the integral,

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \int_0^\infty y e^{-\frac y4} \, dy[/tex]

Integrate by parts, with

[tex]u = y \implies du = dy[/tex]

[tex]dv = e^{-\frac y4} \, dy \implies v = -4 e^{-\frac y4}[/tex]

Then

[tex]\displaystyle \int_{-\infty}^\infty y f(y) \, dy = \frac14 \left(\left(\lim_{y\to\infty}\left(-4y e^{-\frac y4}\right) - \left(-4\cdot0\cdot e^0\right)\right) + 4 \int_0^\infty e^{-\frac y4} \, dy\right)[/tex]

[tex]\displaystyle \cdots = \int_0^\infty e^{-\frac y4} \, dy[/tex]

[tex]\displaystyle \cdots = -4 \left(\lim_{y\to\infty} e^{-\frac y4} - e^0\right) = \boxed{4}[/tex]

Related Questions

!PLEASE ANSWER ASAP! THANK YOU!

if g(n) varies inversely with n and g(n) = 9 when n = 4 then find the value when g(n)=8.

round final answer to the tenths place. if answer is a whole number then put a zero in the tenths place before entering your answer.

Answers

Answer:

Step-by-step explanation:

I'm ASSUMING you want to find n where g(n) = 8

g(n) = a/n

g(4) = 9 = a/4

a = 36

g(n) = 8 = 36/n

n = 36/8 = 4.5

The plans for a shed call for a rectangular floor with a perimeter of 186 ft. The length is two times the width. Find the length and width.

Answers

Answer:

length: 62 ft

width: 31 ft

Step-by-step explanation:

Let w represent the width. Then the length is 2w and the perimeter is ...

P = 2(L+W)

186 = 2(2w +w)

31 = w . . . . . . . . . divide by 6

2w = 2(31) = 62

The length of the shed is 62 feet; its width is 31 feet.

factorise the quadratic expression
pls help me I'll give brainliest
x²+8x-48

Answers

[tex]x^2+8x-48\\\\=x^2 + 12x -4x -48\\\\=x(x+12) -4(x+12)\\\\=(x-4)(x+12)[/tex]

plz help me to answer

Answers

22/3 sorry I accidentally deleted steps

To get to the next term in this sequence, multiply the last term by 2.5. What is the value of the next term?

1, 2.5, 6.25, 15.625, ...

HELP ASAP WILL GIVE BRAINLIEST

Answers

Answer:

39.0625

Step-by-step explanation:

15.625 times 2.5= 39.0625

You're just multiplying each value by 2.5

1 times 2.5= 2.5

2.5 times 2.5= 6.25

6.25 times 2.5= 15.625

and then 15.625 times 2.5= 39.0625

The answer is A but I couldn’t tell you why. If someone know, please let me know.

Answers

Answer:

a.0.311

Step-by-step explanation:

BRAINLIEST ANSWER

What is the second number in the sequence?

Answers

Answer:

Step-by-step explanation:

Let "n" be the second odd number in the sequence

(n - 2) + n + (n + 2) + (n + 4) + (n + 6) = 135

5n + 10 = 135

5n = 125

n = 25

23 + 25 + 27 + 29 + 31 = 135

Change 3/4 to a decimal! Please explain step by step to get marked as brainliest

Answers

Answer:

The answer is 0.75

Step-by-step explanation:

The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.

Another method without a calculator is:

Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.

Step 2: Multiply both top and bottom by that number.

Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)

Example:

Convert 3/4 to a Decimal:

Step 1: We can multiply 4 by 25 to become 100

Step 2: Multiply top and bottom by 25. It gives us 75/100.

Step 3: Write down 75 with the decimal point 2 spaces from the right (because 100 has 2 zeros);

Answer = 0.75

Help me pllllllllllease! I have only got 2 minutes!
When I divide an integer by 15, the remainder is an integer from 0 to 14. When divide an integer by 27, the remainder is an integer from 0 to 26. For instance, if the integer is 100 then the remainders are 10 and 19, which are different. How many integers from 1 to 1000 leave the same remainders after division by 15 and after division by 27?

Answers

Answer:

Two minutes for what???

find answer
the rounded one

Answers

Answer:

229.6 square units

Step-by-step explanation:

19.9×16.8=334.32

19.9-4-4=11.9

16.8-4-4= 8.8

11.9×8.8= 104.72

334.32-104.72= 229.6 sq units

Which expression is equivalent to 53p + (16p + 7p)

Answers

Answer:

u777766665655566667777777777777

76p is the equivalent expression of 53p + (16p + 7p)

What is Expression?

An expression is combination of variables, numbers and operators.

The given expression is 53p + (16p + 7p)

Fifty three times of p plus sixteen p plus seven p.

In the given expression p is the variable and plus is the operator.

We need to find the equivalent expression.

Equivalent expressions are expressions that work the same even though they look different.

53p + (16p + 7p)

76p

Hence, 76p is the equivalent expression of 53p + (16p + 7p)

To learn more on Expressions click:

https://brainly.com/question/14083225

#SPJ6

A line with a slope of 10 passes through the point (0,4). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.

Answers

Answer:

y=10x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-4=10(x-0)

y-4=10(x)

y-4=10x

y=10x+4

Help hep help help math math

Answers

Answer:

-2

Step-by-step explanation:

the input, or domain is always replacing x

y=-2x+6

y=-2(4)+6

y=-8+6

y=-2

brainless for the person who gets this right!
which expression its equivalent

Answers

D

If we expand the parentheses, and multiply everything inside with everything outside, we get

4•6x + 4•11
Which is equal to 24x + 11

In AJKL, j = 75 cm, k = 23 cm and

Answers

Answer:

The length of side j is 11.85cm

Step-by-step explanation:

Given that

In triangle JKL,

Side k=LJ=3.7cm

To find side j=KL:

By using sine rule,

We can write as

Using property of triangle,

Thus,

The length of side j is 11.85cm

Answer them all please

Answers

Answer:

see the attachment

i hope it helps u ✌️✌️✌️☠️

a) The highest common factor and the least common multiple are 12 and 48, respectively.

b) The highest common factor and the least common multiple are 12 and 72, respectively.

c) The highest common factor and the least common multiple are 8 and 160, respectively.

d) The highest common factor and the least common multiple are 12 and 48, respectively.

e) The highest common factor and the least common multiple are 14 and 840, respectively.

Procedure - Determination of the Highest Common Factor and the Least Common Multiple of two integers

In this question we must determine the highest common factor and the least common multiple of two integers.

The highest common factor consists in the maximum product of common prime numbers, of the two numbers that divides it, and the least common multiple consists in the product of prime numbers, common and not, of the two numbers, that creates a product that it is greater or equal to the greater integer.

Now, we proceed to determine the numbers for each case:

a) 12 and 48