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# Probability Density Function

### Probability density function represented

The incomplete probability distribution table at the right is representative of some discrete random variable x. Answer the following: x P(X=x) (a) Determine the value that is missing in the table. (Hint: what are the requirments for a probability distribution?) 0 0.29 1 2 0.24 (b) Find the probab

### A particle is distributed along the positive x axis with a probability density.....

Please see the attached file for the fully formatted problems. 1. A particle is distributed along the positive x axis with a probability density P(x) = C x2 exp(-(x/a)2). Determine it's average coordinate <x>, and the fluctuation <&#61508;x2> ; where <&#61508;x>= x-<x> 2. The coordinate of a particle is distributed

### Uniform Distributions and Probability Density Functions

Let A be a random variable that is uniformly distributed over (0,1). Find the pdf of B = A^(1/n). See the attached file.

### Continuous Random Variable and Probability Density Function

Let X denote a continuous random variable with probability density function f(x) = kx^3/15 for 1≤ X ≤ 2. a. Determine the value of the constant k. b. Determine the probability that X > 1.5. c. Determine the cumulative distribution function F(x) and state the values of F(x) at x = 0.5, 1.5, and 2.5.

### Probability density function for random variable

The weekly demand X for copies of a popular word processing program at a computer store has the following probability distribution shown here. X: 0 1 2 3 4 5 Px(x): .06 .14 .16 .14 .12 .10 X: 6 7 8 9 10 Px(x): .08 .07 .06

### Probability Unit Contamination Particles

The number of failures of a unit from contamination particles on the unit is a Poisson random variable with a mean of 0.02 failures per hour. a.) What is the probability that the instrument does not fail in an 8-hour shift? b.) What is the probability of at least one failure in a 24-hour day? Samples are defective in 1% o

### 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 >

### Bivariate Probability Distribution and Joint Density Functions

Let X1 and X2 have the joint density function given by: f(x1,x2) = { 3*x1 0<=x2<=x1<=1 0 elsewhere} a) Find E(X2) b) Find E(X2|X1 = x1) c) Use the conditional expectation formula: E(X1) = E[E(X1|X2)] to find E(X2)

### Probability Problems Procedure Computations

Need step by step answer to Q no. 2,3 and 7. Please note for Q#3 that only the exponent of e is divided by 2b^2, not the entire numerator as it seems in question. See attached file for full problem description.

### Find the probability that a randomly selected adult has an IQ greater than 131.5

Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of 15. Draw a graph. Find the probability that a randomly selected adult has an IQ greater than131.5 (the requirement for membership in the Mensa organization).

### Random variable and probability density function

See attached file for full problem description. Let X be a random variable with probability density function 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?

### Normal Probability Distribution

Probability density calculation for Normal variable. See attached file for full problem description.

### 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

### Probability and Marginal Density Function

Let X and Y have joint probability density function f(x,y) (s,t) = 20e^-(4s+5t) for 0 < s, and 0 < t. Find (a) Pr{X = Y} (b) Pr{min(X,y) > 1/5}, (c) Pr {X < Y}, (d) the marginal probability density function of X, and (e) E[XY].

### 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: ---

### Calculate PDF of composite random variables and processes

Calculate PDF of composite random variables and processes. See attached file for full problem description.

### 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

### Jointly Distributed Random Variables : Joint Probability Density Functions

Suppose X and Y are jointly continuous with joint pdf f(x,y)=xe^[-x(1+y)], x,y>0. a) What are the marginal pdf's of X and Y? b) What is the conditional pdf of X given Y=y? c) What is the conditional pdf of Y given X=x? d) What is the distribution of Y given X=x called?

### 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

### Calculations for Integrating the Density Function

The density function of a random variable X is f(x) = e^-x x >= 0 = 0 otherwise Find (a) E(X), (b) E(X²), (c) E{(X-1)²}. Please see attached for full question.

### Density Function Question - f(x) = 3x^2?

Let X be a random variable defined by the given density function f(x) = 3x^2 0 <= x <= 1 = 0 otherwise Find (a) E(X), (b) E(3X-2) and (c) E(X^2). See the attached file.

### Probability Density Function - Complex Gaussian Noise

Referencing the attached: NOTE: The solution for part B is highlighted within the attached file. Re-stated here it is: p(I) = ( 1 / < I > ) exp ( - I / < I > ) I'm not sure how. Part a, is essentially: Integral (infinity, 0) p(I, theta) di. which according to my calculation equals: - 1 --