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Triss [41]
3 years ago
7

Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 ,

7 ] , find the expected value, the mean, the variance and the standard deviation.
Mathematics
1 answer:
kenny6666 [7]3 years ago
4 0

Answer:

E(X) =\int_{4}^7 \frac{1}{3} x

E(X) = \frac{1}{6} (7^2 -4^2) = 5.5

Now we can find the second moment with this formula:

E(X^2) =\int_{4}^7 \frac{1}{3} x^2

E(X^2) = \frac{1}{9} (7^3 -4^3) = 31

And the variance for this case would be:

Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75

And the standard deviation is:

Sd(X)= \sqrt{0.75}= 0.866

Step-by-step explanation:

For this case we have the following probability density function

f(x)= \frac{1}{3}, 4 \leq x \leq 7

And for this case we can find the expected value with this formula:

E(X) =\int_{4}^7 \frac{1}{3} x

E(X) = \frac{1}{6} (7^2 -4^2) = 5.5

Now we can find the second moment with this formula:

E(X^2) =\int_{4}^7 \frac{1}{3} x^2

E(X^2) = \frac{1}{9} (7^3 -4^3) = 31

And the variance for this case would be:

Var(X)= E(X^2) -[E(X)]^2 = 31 -(5.5)^2 = 0.75

And the standard deviation is:

Sd(X)= \sqrt{0.75}= 0.866

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Let f(x) = 3 * sqrt(x) + 7. Define g$to be the inverse of f.
aliina [53]

By using the definition of inverse functions, we will see that:

g(g(f(f(f(36))))) = f(36) = 25.

<h3>What are inverse functions?</h3>

Two functions f(x) and g(x) are inverses if:

f( g(x) ) = x

g( f(x) ) = x

Then we can rewrite:

g(g(f(f(f(36)))))

First, we can see that:

g(f(f(f(36)))) = f(f(36))

Replacing that in our expression, we get:

g(g(f(f(f36))))) = g(f(f(36)))

And the above expression is equal to f(36), to be sure of that, let's replace:

u = f(36)

Then we can rewrite:

g(f(f(36))) = g(f(u))

And by definition, the above thing is equal to u:

g(f(u)) = u = f(36).

Finally, we conclude that:

g(g(f(f(f(36))))) = f(36) = 3*√36 + 7 = 3*6 + 7 = 25

If you want to learn more about inverse functions, you can read:

brainly.com/question/12220962

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Step-by-step explanation:

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