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5. (15 pts) The length of a jujube leaf in my garden is a random variable...
5 The length (in centimeters) of the leaf of a certain plant is a continuous random...
5 The length (in centimeters) of the leaf of a certain plant is a continuous random variable with probability density function defined by f(x) = for x in 14 [3, 5.8]. Find the mean of the distribution, the standard deviation of the distribution, and the probability that the random variable is between the mean and 1 standard deviation above the mean. The mean of the distribution is cm. (Round to one decimal place as needed.) cm. The standard deviation of...
#5 please 2. Find the probability distribution function for the random variable representing picking a random real numb...
#5 please
2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation...
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with ...
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF
Problem 5. Let X...
6) If the probability density function of a continuous random variable X is f(x) =x/8 when...
6) If the probability density function of a continuous random variable X is f(x) =x/8 when 3<x < 5, f(x)=0 otherwise a) Find the expected value of this distribution. b) Find the variance of this distribution. c) Find the 25th percentile of this distribution.
Consider a continuous random variable X with the following probability density function: Problem 2 (15 minutes)...
Consider a continuous random variable X with the following
probability density function:
Problem 2 (15 minutes) Consider a continuous random variable X with the following probability density function: f(x) = {& Otherwise ?' 10 otherwise? a. Is /(x) a well defined probability density function? b. What is the mathematical expectation of U (2) = x (the mean of X, )? c. What is the mathematical expectation of U(z) = (1 - 2 (the variance of X, oº)?
PLEASE ANSWER ALL QUESTION 1 1 points Save Answer A random variable is a uniform random...
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QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density...
please answer all 3 a The length of time (in years) until a particular radioactive particle...
please answer all 3
a The length of time (in years) until a particular radioactive particle decays is a random variablet with probability density function defined by f(t) = 8 e - 8t fort in [0, 0o). Find the mean of the distribution, the standard deviation of the distribution, and the probability that the random variable is between the mean and 1 standard deviation above the mean. b The length (in centimeters) of the leaf of a certain plant is...
3 The probability density function of a random variable on the interval [9, 16] is f(x)...
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
(8pts.) Let random variable X be the length of a side of a square. Suppose that...
(8pts.) Let random variable X be the length of a side of a square. Suppose that X has the probability density function, f(x) = 1 / 2 0 < 252. (a) Find P(X < 0.5). (b) What is the variance of X? (C) Let Y be the volume of a cube built with the length of each side being X. Note that Y = X3. What is the expected volume of the cube, E(Y)?
5 The length (in centimeters) of the leaf of a certain plant is a continuous random variable with probability density function defined by f(x) = for x in 14 [3, 5.8]. Find the mean of the distribution, the standard deviation of the distribution, and the probability that the random variable is between the mean and 1 standard deviation above the mean. The mean of the distribution is cm. (Round to one decimal place as needed.) cm. The standard deviation of...
#5 please
2. Find the probability distribution function for the random variable representing picking a random real number between -1 and 1. (This is a piecewise defined function.) 3. Compute the mean of the random variable with density function if x>0 ed f(r) = if r < 0. 0 4. Compute the mean of the random variable with density function 2e (1 - cos x) if x >0 if r<O. f (x) = 5 Compute the variance and standard deviation...
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF
Problem 5. Let X...
Consider a continuous random variable X with the following
probability density function:
Problem 2 (15 minutes) Consider a continuous random variable X with the following probability density function: f(x) = {& Otherwise ?' 10 otherwise? a. Is /(x) a well defined probability density function? b. What is the mathematical expectation of U (2) = x (the mean of X, )? c. What is the mathematical expectation of U(z) = (1 - 2 (the variance of X, oº)?
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QUESTION 1 1 points Save Answer A random variable is a uniform random variable between 0 and 8. The probability density is 1/8, when 0<x<8 and O elsewhere. What is the probability that the random variable has a value greater than 2? QUESTION 2 1 points Save Answer The total area under a probability density curve of a continuous random variable is QUESTION 3 1 points Save Answer X is a continuous random variable with probability density...
please answer all 3
a The length of time (in years) until a particular radioactive particle decays is a random variablet with probability density function defined by f(t) = 8 e - 8t fort in [0, 0o). Find the mean of the distribution, the standard deviation of the distribution, and the probability that the random variable is between the mean and 1 standard deviation above the mean. b The length (in centimeters) of the leaf of a certain plant is...
3 The probability density function of a random variable on the interval [9, 16] is f(x) = x. Find the following values. a. Find the expected value The expected value is (Round to two decimal places as needed.) b. Find the variance. The variance is (Round to two decimal places as needed.) c. Find the standard deviation The standard deviation is (Round to two decimal places as needed.) d. Find the probability that the random variable has a value greater...
2. Let y=-3x+4.For the case that X is Gaussian random variable of normal distribution given as N (0,4), find the probability density function of Y. What is the mean and variance of Y
(8pts.) Let random variable X be the length of a side of a square. Suppose that X has the probability density function, f(x) = 1 / 2 0 < 252. (a) Find P(X < 0.5). (b) What is the variance of X? (C) Let Y be the volume of a cube built with the length of each side being X. Note that Y = X3. What is the expected volume of the cube, E(Y)?
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