1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Alecsey [184]
3 years ago
7

Suppose X has an exponential distribution with mean equal to 23. Determine the following:

Mathematics
1 answer:
e-lub [12.9K]3 years ago
5 0

Answer:

a) P(X > 10) = 0.6473

b) P(X > 20) = 0.4190

c) P(X < 30) = 0.7288

d) x = 68.87

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

f(x) = \mu e^{-\mu x}

In which \mu = \frac{1}{m} is the decay parameter.

The probability that x is lower or equal to a is given by:

P(X \leq x) = \int\limits^a_0 {f(x)} \, dx

Which has the following solution:

P(X \leq x) = 1 - e^{-\mu x}

The probability of finding a value higher than x is:

P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}

Mean equal to 23.

This means that m = 23, \mu = \frac{1}{23} = 0.0435

(a) P(X >10)

P(X > 10) = e^{-0.0435*10} = 0.6473

So

P(X > 10) = 0.6473

(b) P(X >20)

P(X > 20) = e^{-0.0435*20} = 0.4190

So

P(X > 20) = 0.4190

(c) P(X <30)

P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288

So

P(X < 30) = 0.7288

(d) Find the value of x such that P(X > x) = 0.05

So

P(X > x) = e^{-\mu x}

0.05 = e^{-0.0435x}

\ln{e^{-0.0435x}} = \ln{0.05}

-0.0435x = \ln{0.05}

x = -\frac{\ln{0.05}}{0.0435}

x = 68.87

You might be interested in
Convert 5 feet to inches there are 12 inches in 1 foot
ladessa [460]

Answer:

60

Step-by-step explanation:

12*5=60

12 inches in a foot, you have 5 feet so 12*5=60

3 0
3 years ago
Read 2 more answers
A sample of 5 buttons is randomly selected and the following diameters are measured in inches. Give a point estimate for the pop
Helen [10]

Answer:

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

But we need to calculate the mean with the following formula:

\bar X = \frac{\sum_{i=1}^n X_I}{n}

And replacing we got:

\bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072

And for the sample variance we have:

s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003

And thi is the best estimator for the population variance since is an unbiased estimator od the population variance \sigma^2

E(s^2) = \sigma^2

Step-by-step explanation:

For this case we have the following data:

1.04,1.00,1.13,1.08,1.11

And in order to estimate the population variance we can use the sample variance formula:

s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}

But we need to calculate the mean with the following formula:

\bar X = \frac{\sum_{i=1}^n X_I}{n}

And replacing we got:

\bar X = \frac{ 1.04+1.00+1.13+1.08+1.11}{5}= 1.072

And for the sample variance we have:

s^2 = \frac{(1.04-1.072)^2 +(1.00-1.072)^2 +(1.13-1.072)^2 +(1.08-1.072)^2 +(1.11-1.072)^2}{5-1}= 0.00277\ approx 0.003

And thi is the best estimator for the population variance since is an unbiased estimator od the population variance \sigma^2

E(s^2) = \sigma^2

3 0
3 years ago
A baby eats 8 oz. of formula in 15 min.at this rate,how much formula can the baby eat in 2 hours​
Readme [11.4K]

Answer:

The Answer is: 64 oz.

Step-by-step explanation:

Convert 2 hours to minutes and then by 15 minutes:

(2 * 60) / 15 =

120 / 15 = 8

Multiply 8 time 8 = 64 oz.

4 0
2 years ago
Dddddddddddddddddddddddd
Ierofanga [76]

Answer:

dddddddddddddddddddddddd could be rewritten as d^24 because d*d*d*d*d*d*d... = d^24

Step-by-step explanation:

When we multiply all of the d's together we get d^{24}.

4 0
3 years ago
Read 2 more answers
Four times the difference of a number and seven is 32
disa [49]
As a formula, you're saying 4*(n-7)=32

This solves to n-7 = 8, so n=15
5 0
3 years ago
Other questions:
  • Please answer correctly, will mark brainliest answer !!!
    7·2 answers
  • Match the estimated value of each expression with its position on the number line ​
    14·2 answers
  • The price of a gallon of gas was $3.23 one week and $3.15 the next. What is the percent of decrease for the price of a gallon of
    15·1 answer
  • Write a number that has four digits with same number in all places, such as 4,444. circle the digit with the greatest value. und
    10·1 answer
  • What are the constant terms in the expression?<br><br> 6x2+7xy+3+96x2+7xy+3+9
    8·2 answers
  • 0.66×1691 = type a Integer or a decimal estimate the answer by first rounding the first number to the nearest tenth and the seco
    14·1 answer
  • Plz explain
    9·2 answers
  • A printer need to make a poster that will have a total poster area of 200 in^2 and will have 1 inch margins on the sides, a 2-in
    15·1 answer
  • Use the points to describe the data and determine the line of best fit.
    12·1 answer
  • Express 8% as a decimal fraction​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!