F(x)=0.25x+0.5 x < -2 -2≤x<2 25x Determine the probability that the random variable X is greater than -1.
F(x)=0.25x+0.5 x < -2 -2≤x<2 25x Determine the probability that the random variable X is greater than -1.
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Question
![Suppose that the cumulative distribution function of the random variable X is
[o
x < -2
F(x)=0.25x+0.5
-2<x<2
25x
Determine the probability that the random variable X is greater than -1.
Suppose that the probability density function of a random variable is given as below.
Determine the mean and variance of X.
f(x)= 0.125 for 0<x< 8
In an experiment, we are measuring a random variable that is continuous and it follows the
uniform distribution. Possible range of this variable is between 1.5 and 5.5. Determine the
probability that a measurement is below 2.5.
Use Appendix A. Table III to determine the following probabilities for the standard normal
random variable Z:
P(Z <2); P(Z >-1.15); P(-2.12<Z<0.76)
Assume that Z has a standard normal distribution. Use Appendix Table III to determine the
value for z that solves each of the following:
P(Z > 2) = 0.8; P(Z < z) = 0.25
Suppose that for a random variable X, we have this characteristic: N(10, 4). Determine the
probability that this variable is between -2 and 6. Also, determine the value for which the
probability that the random variable X is greater than this value is 0.9.
Suppose that the time to failure (in hours) of fans in a personal computer can be modeled as
a Poisson process with average of 0.0003 failures per hour. What is the probability that a fan
will last at least 10,000 hours?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd42bce21-b8fa-4bfa-81d4-f30b17b60c59%2F4a04ac09-e757-4731-9378-5beed7c4d059%2F6nuj5ld_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Suppose that the cumulative distribution function of the random variable X is
[o
x < -2
F(x)=0.25x+0.5
-2<x<2
25x
Determine the probability that the random variable X is greater than -1.
Suppose that the probability density function of a random variable is given as below.
Determine the mean and variance of X.
f(x)= 0.125 for 0<x< 8
In an experiment, we are measuring a random variable that is continuous and it follows the
uniform distribution. Possible range of this variable is between 1.5 and 5.5. Determine the
probability that a measurement is below 2.5.
Use Appendix A. Table III to determine the following probabilities for the standard normal
random variable Z:
P(Z <2); P(Z >-1.15); P(-2.12<Z<0.76)
Assume that Z has a standard normal distribution. Use Appendix Table III to determine the
value for z that solves each of the following:
P(Z > 2) = 0.8; P(Z < z) = 0.25
Suppose that for a random variable X, we have this characteristic: N(10, 4). Determine the
probability that this variable is between -2 and 6. Also, determine the value for which the
probability that the random variable X is greater than this value is 0.9.
Suppose that the time to failure (in hours) of fans in a personal computer can be modeled as
a Poisson process with average of 0.0003 failures per hour. What is the probability that a fan
will last at least 10,000 hours?
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