2.5.12. The length of time that an individual talks on a long-distance telephone call has been...
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The length of time that an individual talks on a long-distance telephone call has been found to be of a random nature. Let X be the length of the talk; assume it to be a continuous random variable with probability density function given by f(x)- 0, elsewhere Find (a) The value of a that makes f(x a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 minutes, (i) less than...
9. Let X denote the length in minutes of a long-distance telephone conversation. Assume that the density for X is given by (ax) 1/20)e-20x0 Verify that f is a density for a continuous random variable.
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
Assume the length X in minutes of a particular type of telephone conversation is a random variable with probability density function f(x) = {1/5 e^x/5, x > 0 0, elsewhere (a) Determine the mean length E (X) of this type of telephone conversation. (b) Find the variance and standard deviation of X. (c) Find E [(X + 5)^2].
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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...
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...
The distance X between trees in a given forest has a probability density function given f (x) cex/10, x >0, and zero otherwise with measurement in feet i) Find the value of c that makes this function a valid probability density function. [4 marks] ii) Find the cumulative distribution function (CDF) of X. 5 marks What is the probability that the distance from a randomly selected tree to its nearest neighbour is at least 15 feet. iii) 4 marks) iv)...
I am studying Continuous Random Variables.
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II.1 Let X be a continuous random variable with the density function 1/4 if x E (-2,2) 0 otherwise &Cx)={ Find the probability density function of Z = X density function fx. Find the distribution function Fy (t) and the density function f,(t) of Y=지 (in terms of Fx and fx).
II.1 Let X be a continuous random variable with the density...
Question 1 A continuous random variable X which represents the amount of sugar (in kg) used by a family per week, has the probability density function c(x-102-x) 1sxs2 ; otherwise (0) (ii) (ii) Determine the value of c. Obtain cumulative distribution function Find P(X < 1.2). Consider the following cumulative distribution function for X. 06 0.8 1.0 Fx) 0.9 (i) Determine the probability distribution. (ii) Find P(X 1). (ii) Find P(OX5) Question 3 Consider the following pdf otherwise (i) (ii)...
both A and B, B
A statistical analysis of 1,000 long-distance telephone calls made by a company indicates that the length of these calls is normally distributed, with μ-290 second 50 seconds. Complete parts (a) through (d). EE Click here to view page 1 of the cumulative standardized normal distribution table. E Click here to view page 2 of the cumulative standardized normal distribution table. a. What is the probability that a call lasted less than 190 seconds? The probability...