The points on the graph of the function y=3+f(x-1) can be obtained from the points on y=f(x) by a shift of:

Let X denote the distance (m) that an animal moves from its birth site to the first territorial vacancy it encounters. Suppose t

andrezito [222]

Answer and Step-by-step explanation: For an exponential distribution, the probability distribution function is:

f(x) = λ. $e^{-\lambda.x}$

and the cumulative distribution function, which describes the probability distribution of a random variable X, is:

F(x) = 1 - $e^{-\lambda.x}$

(a) Probability of distance at most 100m, with λ = 0.0143:

F(100) = 1 - $e^{-0.0143.100}$

F(100) = 0.76

Probability of distance at most 200:

F(200) = 1 - $e^{-0.0143.200}$

F(200) = 0.94

Probability of distance between 100 and 200:

F(100≤X≤200) = F(200) - F(100)

F(100≤X≤200) = 0.94 - 0.76

F(100≤X≤200) = 0.18

(b) The mean, E(X), of a probability distribution is calculated by:

E(X) = $\frac{1}{\lambda}$

E(X) = $\frac{1}{0.0143}$

E(X) = 69.93

The standard deviation is the square root of variance,V(X), which is calculated by:

σ = $\sqrt{\frac{1}{\lambda^{2}} }$

σ = $\sqrt{\frac{1}{0.0143^{2}} }$

σ = 69.93

Distance exceeds the mean distance by more than 2σ:

P(X > 69.93+2.69.93) = P(X > 209.79)

P(X > 209.79) = 1 - P(X≤209.79)

P(X > 209.79) = 1 - F(209.79)

P(X > 209.79) = 1 - (1 - $e^{-0.0143*209.79}$ )

P(X > 209.79) = 0.0503

(c) Median is a point that divides the value in half. For a probability distribution:

P(X≤m) = 0.5

$\int\limits^m_0 f({x}) \, dx$ = 0.5

$\int\limits^m_0 {\lambda.e^{-\lambda.x}} \, dx$ = 0.5

$\lambda.\frac{e^{-\lambda.x}}{-\lambda}$ = $-e^{-\lambda.x} + e^{0}$

$1 - e^{-\lambda.m}$ = 0.5

$-e^{-\lambda.m}$ = - 0.5

ln( $e^{-0.0143.m}$ ) = ln(0.5)

-0.0143.m = - 0.0693

m = 48.46

6 0

4 years ago

Which center processes aluminum faster, and why?

garri49 [273]

Answer:

Recycling

Step-by-step explanation:

because i see recyling bins everywhere

7 0

2 years ago

Without multiplying, determine the sign of the product (−247,634)(183,758).

adoni [48]

Negative bc negative times positive is negative

6 0

4 years ago

You work at Initech for a year. Your annual salary income is $38,000. You received a 3% salary increase. What is your NEW salary

sdas [7]

$49,400. If you multiply the income (38,000) by the salary increase (3%=0.3), then you get 49,400. Good Luck!

4 0

3 years ago

Write an equation in point slope form of the line passes through the given point and has the given slope

Novay_Z [31]

Answer:

Step-by-step explanation:

y - y₁ = m ( x - x₁)

y - 5 = - 3 (x - 12)

y - 5 = -3x + 36

3x + y = 36 + 5

3x + y = 41

y = -3x + 41

6 0

4 years ago