Question

In: Statistics and Probability

For each probability and percentile problem, draw the picture. Let X ~ Exp(0.15). a. Sketch a...

For each probability and percentile problem, draw the picture.

Let X ~ Exp(0.15).

a. Sketch a new graph, shade the area corresponding to P(X < 7), and find the probability. (Round your answer to four decimal places.)

b.Sketch a new graph, shade the area corresponding to P(2 < X < 7), and find the probability. (Round your answer to four decimal places.)

c. Sketch a new graph, shade the area corresponding to P(X > 7), and find the probability. (Round your answer to four decimal places.)

d. Sketch a new graph, shade the area corresponding to the 40th percentile, and find the value. (Round your answer to two decimal places.)

e. Find the average value of X. (Round your answer to two decimal places.)

Solutions

Expert Solution

The CDF of the distribution is

a) The area corresponding to P(X < 7) is shaded below.

The probability is

b) The area corresponding to P(2 < X < 7)is shaded below.

The probability is

c) The area corresponding to P(X > 7) is shaded below.

The probability is

d) The 40-the percentile is

The region is shaded below.

e) The average value of the exponential distribution is

orchestra answered 1 year ago

Next > < Previous

Related Solutions

For each probability and percentile problem, draw the picture. Births are approximately uniformly distributed between the...

For each probability and percentile problem, draw the picture. Births are approximately uniformly distributed between the 52 weeks of the year. They can be said to follow a uniform distribution from one to 53 (spread of 52 weeks). part G: Enter an exact number as an integer, fraction, or decimal. P(2 < x < 9) = Part H: Find the probability that a person is born after week 42. (Enter an exact number as an integer, fraction, or decimal.) Part...

2. Let X ~ exponential(lambda). Find the 2.5th percentile and the 97.5th percentile of X, that...

2. Let X ~ exponential(lambda). Find the 2.5th percentile and the 97.5th percentile of X, that is, find x*subscript*.025 and x*subscript*.975

Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z...

Let X ∼Exp(1), Y ∼Exp(2) be independent random variables. (a) What is the range of Z := X + Y ? (b) Find the pdf of Z. (c) Find MZ(t). (d) Let U = e Y . What is the range of U? (e) Find the pdf of U|X.

Let X be a random variable. Suppose X ∼ Exp(0.5). The area under the pdf of...

Let X be a random variable. Suppose X ∼ Exp(0.5). The area under the pdf of the Exp(0.5) distribution above the interval [0, 2] is 0.6321. What is the value of the cumulative distribution function FX of X at x = 2?

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y =...

Let X ~ exp(λ) MGF of X = λ/(1-t) a) What is MGF of Y = 3X b) Y has a common distribution, what is the pdf of Y? c) Let X1,X2,....Xk be independent and identically distributed with Xi ~ exp(λ) and S = Σ Xi (with i = 1 below the summation symbol, and k is on top of the summation symbol). What is the MGF of S? d) S has a common distribution. What is the pdf of...

Find the (probability generating function) p.g.f.’s of the following distributions:[3+3=6] •P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,...,...

Find the (probability generating function) p.g.f.’s of the following distributions:[3+3=6] •P(X=x) =(exp(−λ)λ^x)/((1−exp(−λ))x!) , for x= 1,2,3,..., and λ >0. •P(X=x) =((pq)^x)(1−q^(N+1))^−1,for x= 0,1,..., N; where 0 < p < 1, p+q= 1.

For each problem, write an R code to compute each probability. (a) Binomial Distribution: X ~...

For each problem, write an R code to compute each probability. (a) Binomial Distribution: X ~ Bin(10, 0.7) (i) P(X = 2) (ii) P(X < 2) (iii) P(X > 2) (iv) P(1 < X < 7) (b) Normal Distribution: X ~ N(0, 4). Note that variance is 4 and, hence, the standard deviation is 2. (i) P(X < 3) (ii) P(X > 3) (iii) P(1 < X < 3) (c) Choose either (a) or (b) and interpret the results in...

Independent trials, each of which is a success with probability p, are successively performed. Let X...

Independent trials, each of which is a success with probability p, are successively performed. Let X denote the first trial resulting in a success. That is, X will equal k if the first k −1 trials are all failures and the kth a success. X is called a Geometric random variable (google it). Determine the moment generating function of X.

1. For each of the cases that follow, draw a picture of the system being described...

1. For each of the cases that follow, draw a picture of the system being described and list as many properties of the equilibrium state as you can, especially the constraints placed on the equilibrium state of the system by its surroundings. a. The system is placed in thermal contact with a thermostatic bath maintained at temperature T. b. The system is contained in a constant-volume container and thermally and mechanically isolated from its surroundings. c. The system is contained...

x P(x) 0 0.15 1 0.1 2 0.3 3 0.45 Find the mean of this probability...

x P(x) 0 0.15 1 0.1 2 0.3 3 0.45 Find the mean of this probability distribution. Round your answer to one decimal place. 2 x P(x) 0 0.05 1 0.15 2 0.25 3 0.55 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places 3 2.36 Is it worth it?: Andy is always looking for ways to make money fast. Lately, he has been trying to make money by gambling. Here is...

Subjects