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Probability Density Function

Normal probability calculation

#1 The average number of customer complaints at the Full Moon Motel is five per day. Find the probability that on a typical day, the motel will receive a) eight complaints b) at least two complaints #2 Demand for a product is normal, with mean being 400 and standard deviation being 25 units. Find a) Pr (demand >

Probability, Cumulative Distribution Function

Let X be a random variable with probability density f(x) = c(1-x^2), if -1<x<1 = 0, if otherwise Determine the value of the constant , and find the cumulative distribution function of X

Distribution of Minimum of Uniform distribution

(See attached file for full problem description with proper symbols and equations) Let ......, be identically distributed random variables, each having a distribution function F(x). Let M = min . 1. Find the distribution function of M. 2. Now suppose F is the uniform distribution over . What is the probability density

Joint and Marginal Distribution Functions Problem

Let X and Y be continuous random variables. (i) Show that if X and Y are independent, they they are uncorrelated. (ii) Prove that X + Y and X - Y are uncorrelated if and only if X and Y have the same variance. Suppose that the joint probability density function of the continuous random variables U and V is given by f

Joint probability density function

(See attached file for full problem description with equations) --- 53. Given that the joint pdf of the random variables X and Y is defined by (i) Find the number k. (ii) Find the marginal pdf's fX and fY. Are X and Y independent? (iii) Calculate the probabilities: ---

Joint and Marginal Probability Density Functions of Independent

Let X, Y be independent, standard normal random variables, and let U = X + Y and V = X - Y. (a) Find the joint probability density function of (U, V) and specify its domain. (b) Find the marginal probability density function of U and V specifying the domain in each case. (c) Explain why U and V are independent Joint probab

Joint Uniform Distribution and Probability Density Function

10. ... Suppose that X and Y are independent with each uniformly distributed on the interval ... a. What is the joint pdf? b. What is the probability that they both arrive between ... c. If the first one to arrive will wait only 10 minutes before leaving to eat elsewhere, what is the probability ... (Please see attachmen

Jointly Distributed Random Variables : Marginal Probability

12. Two components of a minicomputer have the following joint pdf for their useful life times X and Y: (see attachment) a. What is the probability that the lifetime X of the first component exceeds 3? b. What are the marginal pdf's of X and Y? Are the two lifetimes independent? Explain. c. What is the probability that the l

Probability density function ..

4. The probability density function if X, the lifetime of a certain type of electronic device (measured in hours} is given by: f(x) = 10/x^2 for x>10 and =0 for x<=10 (a) Find P {X > 20} (b) What is the cumulative distribution function of X? (c) What is the probability that of 6 such types of devices at least 3 will

The problem is from probability class.

#4. The probability density function of X, the lifetime of a certain type of electronic device (measured in hours), is given by f (x) = 10/x2 x > 10 f (x) = 0 x &#8804; 10 (a) Find P{X > 20}. (b) What is cumulative distribution function of X? .. (see attachment)

Probability density function problem

# 3. Consider the function f (x) = C ( 2x - x³) 0 < x < 5/2 f (x) = 0 otherwise. Could f be a probability density function? If so, determine C. Repeat if f (x) were given by f (x) = C ( 2x - x²) 0 < x < 5/2 f (x) = 0 otherwise.

Joint Density

3. The joint probability density function of X and Y is given by f(x, y) =6/7 (x2 + xy/2 ), 0 < x < 1, 0 < y < 2. (a) Verify that this is indeed a joint density function. (b) Compute the density function of X. (c) Find P(X > Y ). (d) Find P(Y > 1/2|X < 1/2). (e) Find E(X). (f) Find E(Y ). Please see attachment for

Probability density function

Assume that X is a random variable with a probability density function f(x)=cx^2, -1<x<1 0, otherwise Find the constant c;

Radial probability of hydrogen wave function

Show that the radial probability density for n=2, l=1, m=0 for the hydrogen atom can be written as: P(r) = A*cos(q)^2*r^4*exp(-r/a) Show that the most likely position of the electron is found at r=4a See attached file for full problem description.

Functions of Random Variables: Distribution Functions

See the attached file. 1) Let Y be a random variable with a density function given by f(y1) = 3/2y^2 , -1 <y1<1 f(y1) = 0, elsewhere a) find the density function of U1 = 3Y using the method of distribution. b) find the density function of U2 = 3-Y using the method of distribution. c) find the density functi

Median Integration

Solve the median for the probability density function in the attached file 'Median.doc'.

Joint and Marginal Probabilities

Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2. a) Find the joint density of Y1 and Y2 b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).

Probability distribution for discrete random variables

From past experience, an automobile insurance company knows that a given automobile will suffer a total loss with probability .02, a 50% loss with probability .08, or a 25% loss with probability .15 during a year. What annual premium should the company charge to insure a $10,000 automobile, if it wishes to "break even" on all p

Probability of Absence Symptoms

Epidemiologists at a medical center in the Northeast are interested in the etiology of anthracosis ("Black lung" disease), caused by the inhalation of coal dust. All the coal miners in a particlar cummunity were screened and classified according to their length of employment in the coal mines and whether symptoms of anthracosis

List the simple events associated with this experiment.

A major department store chain is planning to open a store in a new city. Five cities are being considered: Boston, Atlanta, Dallas, Cleveland, and Los Angeles. A. List the simple events associated with this experiment. B. Assign a probability to each simple event; assuming each city has an equal chance of being selected.

Distributions for Disease Exposure Levels

A rare disease has just broken out. Doctor Johnson is trying to help, but while treating patients he might expose himself to the disease. He takes many precautions, but he doesn't know how much he's been exposed. Let the number x represent Doctor Johnson's exposure level. He doesn't know it for sure, but he assigns a uniform dis

Probability

Here are questions 33 and 34 to assist in answering question 52. 33) Let X be a random variable with probability density f(x)={c(1-x^2), -1<x<1 0 otherwise (a) What is the value of c? (b) What is the cumulative distribution function of X? 34) Let the probability

Microscopic Toolmark Analysis

I am conducting research on microscopic toolmark analysis. If I have a toolmark with 27 striations (lines) of varying spatial relationships (orientations), widths and densities, do I use the combination formula to determine the probablity that another toolmark will by chance have a group of at least eight consecutively matching