9. Let X denote the length in minutes of a long-distance telephone conversation. Assume that the...
Assume the length X, in minutes, of a particular type of telephone conversation is a random variable with probability density function (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+4)2] .
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].
show steps, thanks 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...
2.5.12. 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 0, elsewhere. Find (a) The value of a that makes fx) a probability density function. (b) The probability that this individual will talk (i) between 8 and 12 min, (ii) less than 8 min,i) more...
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
Let T denote the time in minutes for a customer service representative to respond to 10 telephone inquiries. T is uniformly distributed on the interval with endpoints 8 minutes and 12 minutes. Let R denote the average rate, in customers per minute, at which the representative responds to inquiries. 4. Which of the following is the density function of the random variable R on the interval 10 10 12 (B) 3-5 (c) 3r SIn(r) D)7 CE) 2r 10
5. Suppose that the duration (in minutes) of telephone conversations over a 4G network is a contin- uous random variable X with probability density function fx(u) otherwise What is the probability that the duration of the conversation (a) will exceed 5 minutes? (b) will be less than 6 minutes? (c) will be between 5 and 6 minutes? (d) will be less than 6 minutes, given that it was greater than 5 minutes?
Q,: (2 marks) An administrator wanted to study the utilization of long-distance telephone service by a department. One variable of interest (let's call it X) is the length, in minutes, of long-distance calls made during one month. There were 38 calls that resulted in a connection. The length of calls, already ordered from smallest to largest, are presented in the following table. 1.6 1.7 1.8 1.8 1.9 2.1 4.5 4.5 5.9 7.1 7.4 7.5 12.7 15.3 15.5 15.9 15. 9...
4. Assume that the length of time between charges of a particular cell phone is normally distributed with a mean of 8 hours and a standard deviation of 2 hours. Find the probability that the cell phone will last between 5 and 10 hours between charges. 5. Let X be a continuous random variable with the density function f(x) given by f(0) = 2/8 for 0 < x < 4, and f(1) = 0 otherwise. Find the mean p. 6....
please 6 and 7 6. (3.18, 20) A continuous random variable X that can assume values between r = 2 and x = 5 has a density function given by f(x) = 2(1+x)/27. Find the Cumulative Distribution Function F(x). 7. (3.14) The waiting time, in hours, between successive speeders spotted by a radar unit is a continuous random variable with a cumulative distribution function x<0, F(x) = -e-41, x20 Find the probability of waiting between 3 to 7 minutes a)...