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58 1.7.4. Given [11/*(1 + r) dar, where CCC = {: - <3...
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1,...
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
Q 2. The probability density function of the continuous random variable X is given by Shell,...
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise....
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
7.2. Which of the following functions represent a probability density function for a continuous random variable?...
7.2. Which of the following functions represent a probability density function for a continuous random variable? Hint: Check if both rules of a proper probability density function hold. (a) f(z) = 0.25 where 0-1-8. b) f(r) =1/2 where 0 <1<2
97-11. Determine the shear and moment as a function of x, where 0 < 3 m...
97-11. Determine the shear and moment as a function of x, where 0 < 3 m and 3 m < 5 6 m, and then draw the shear and moment diagrams. 30 kNm - 3 m 17 11
2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3...
2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3 0, otherwise. Find the expected value of the random variable X.
2. The cumulative distribution function of X is given by 0, <0 을, 1 x<2 1O...
2. The cumulative distribution function of X is given by 0, <0 을, 1 x<2 1O 3 < 3.5 107 1 3.5 Is X a discrete or continuous random variable? Give the appropriate probability mass or density function of X based on your answer.
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3...
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3 Thus the pdf of X is f(x) = le-ix for 0 < x where = 3. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the dexp function and the R integrate command calculate the expected value of X. c) Using the pexp function find the probability that .4 SX 5.7 d) Calculate the probability...
be a continuous random variable with probability density function 3. Let for 0 r 1 a,...
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a)...
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a) Find the value of the constant C b) Find the probability that X lies between 1/3 and 1
2.6.17. The probability density function of the random variable X is given by r2 21 0<x-1, 6x-2r2-3 (x, 3)2 0 otherwise.
Q 2. The probability density function of the continuous random variable X is given by Shell, -<< 0. elsewhere. f(x) = {&e*, -40<3<20 (a) Derive the moment generating function of the continuous random variable X. (b) Use the moment generating function in (a) to find the mean and variance of X.
2.5.6. The probability density function of a random variable X is given by f(x) 0, otherwise. (a) Find c (b) Find the distribution function Fx) (c) Compute P(l <X<3)
7.2. Which of the following functions represent a probability density function for a continuous random variable? Hint: Check if both rules of a proper probability density function hold. (a) f(z) = 0.25 where 0-1-8. b) f(r) =1/2 where 0 <1<2
97-11. Determine the shear and moment as a function of x, where 0 < 3 m and 3 m < 5 6 m, and then draw the shear and moment diagrams. 30 kNm - 3 m 17 11
2.6.17. The probability density function of the random variable X is given by 6x-21-3 -, 2<x<3 0, otherwise. Find the expected value of the random variable X.
2. The cumulative distribution function of X is given by 0, <0 을, 1 x<2 1O 3 < 3.5 107 1 3.5 Is X a discrete or continuous random variable? Give the appropriate probability mass or density function of X based on your answer.
Problem #3. X is a random variable with an exponential distribution with rate 1 = 3 Thus the pdf of X is f(x) = le-ix for 0 < x where = 3. a) Using the f(x) above and the R integrate function calculate the expected value of X. b) Using the dexp function and the R integrate command calculate the expected value of X. c) Using the pexp function find the probability that .4 SX 5.7 d) Calculate the probability...
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.
EXERCISE (x2+1), where . < 1) A random variable X has the density function f(x)= a) Find the value of the constant C b) Find the probability that X lies between 1/3 and 1
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