4. Cindy is saving for a trip to Hawaii. Each

Two streams flow into a reservoir. Let X and Y be two continuous random variables representing the flow of each stream with join

zlopas [31]

Answer:

c = 0.165

Step-by-step explanation:

Given:

f(x, y) = cx y(1 + y) for 0 ≤ x ≤ 3 and 0 ≤ y ≤ 3,

f(x, y) = 0 otherwise.

Required:

The value of c

To find the value of c, we make use of the property of a joint probability distribution function which states that

$\int\limits^a_b \int\limits^a_b {f(x,y)} \, dy \, dx = 1$

where a and b represent -infinity to +infinity (in other words, the bound of the distribution)

By substituting cx y(1 + y) for f(x, y) and replacing a and b with their respective values, we have

$\int\limits^3_0 \int\limits^3_0 {cxy(1+y)} \, dy \, dx = 1$

Since c is a constant, we can bring it out of the integral sign; to give us

$c\int\limits^3_0 \int\limits^3_0 {xy(1+y)} \, dy \, dx = 1$

Open the bracket

$c\int\limits^3_0 \int\limits^3_0 {xy+xy^{2} } \, dy \, dx = 1$

Integrate with respect to y

$c\int\limits^3_0 {\frac{xy^{2}}{2} +\frac{xy^{3}}{3} } \, dx (0,3}) = 1$

Substitute 0 and 3 for y

$c\int\limits^3_0 {(\frac{x* 3^{2}}{2} +\frac{x * 3^{3}}{3} ) - (\frac{x* 0^{2}}{2} +\frac{x * 0^{3}}{3})} \, dx = 1$

$c\int\limits^3_0 {(\frac{x* 9}{2} +\frac{x * 27}{3} ) - (0 +0) \, dx = 1$

$c\int\limits^3_0 {(\frac{9x}{2} +\frac{27x}{3} ) \, dx = 1$

Add fraction

$c\int\limits^3_0 {(\frac{27x + 54x}{6}) \, dx = 1$

$c\int\limits^3_0 {\frac{81x}{6} \, dx = 1$

Rewrite;

$c\int\limits^3_0 (81x * \frac{1}{6}) \, dx = 1$

The $\frac{1}{6}$ is a constant, so it can be removed from the integral sign to give

$c * \frac{1}{6}\int\limits^3_0 (81x ) \, dx = 1$

$\frac{c}{6}\int\limits^3_0 (81x ) \, dx = 1$

Integrate with respect to x

$\frac{c}{6} * \frac{81x^{2}}{2} (0,3) = 1$

Substitute 0 and 3 for x

$\frac{c}{6} * \frac{81 * 3^{2} - 81 * 0^{2}}{2} = 1$

$\frac{c}{6} * \frac{81 * 9 - 0}{2} = 1$

$\frac{c}{6} * \frac{729}{2} = 1$

$\frac{729c}{12} = 1$

Multiply both sides by $\frac{12}{729}$

$c = \frac{12}{729}$

$c = 0.0165 (Approximately)$

8 0

4 years ago

Raise c to the 3rd power, then triple the result

777dan777 [17]

Step-by-step explanation:

Raise c to the 3rd power:

${c}^{3}$

Triple the amount (Multiply by 3):

$3( {c}^{3} )$

5 0

2 years ago

HELP ASAP FIRST ANSWER GEST BRAINLIEST Evaluate. 25÷5+7-(4×3)

Dovator [93]

Answer:

0, BRAINLIEST PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS PLS

4 0

3 years ago

What is the value of z in the equation 3z + 5 = 4z − 8?

olganol [36]

Answer:

The answer is 13, please let me know if I am wrong

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0

3 years ago

What property can be used to simplify the expression: 27(2p + 4e + 10p + 20)

Gekata [30.6K]

Well, you can use distributive property to solve this question.
27(2p + 4e + 10p + 20)
= 54p + 108 + 270p + 540
= 324p + 648

6 0

3 years ago