1. Given the following probability density function: p(x) = Ae-1(x-a)². (a) Find (x) (b) Find (x?) (c) Find ox (d) Sketch the graph of the probability density.
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A: Here, a = 200,000 and b= 230,000 f(x) =1/(230000-200000) =1/30000
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Q: a. Find E(X) b. Find E(Y) c. Find E(XY)
A: a.The joint probability density function is,
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A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts. In case…
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Q: a) What must c be for the function to be a probability density function? b) Calculate F(1).
A: c can be calculated as:
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- Suppose that the probability density function of the length of computer cables is f (x) = 2x/(32) for x between 0 and 3 meters. Determine the mean of the cable length. Please enter the answer to 2 decimal places.Suppose X is exponentially distributed with mean 2. Let Y = eX. What is the density function of Y?Compare a graph of the normal density function with mean of 0 and standard deviation of 1 with a graph of a normal density function with mean equal to 4 and standard deviation of 1. The graphs would: Have the same height but one would be shifted 4 units to the right. Have no horizontal displacement but one would be flatter than the other. Have no horizontal displacement but one would be steeper that the other.
- The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) = (e-x/1000 )/1000 for x > 0. Determine the the number of hours at which 12% of all components have failed. Please enter the answer to 2 decimal places.Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a) According to Chebychef’s rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(|x − µ| <2 ∗ σ) b) What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?Suppose that the probability density function of the length of computer cables is f (x) = 2x/(52) for x between 0 and 5 meters. Determine the standard deviation of the cable length. Please enter the answer to 2 decimal places.
- Suppose the duration (in hours) of a certain valve is a random variableX with density function f(x) = 648x−4 for x > 6, and zero otherwise. What's the time expected life (in hours) of this valve?With the known values of a = 200,000 and b = 230,000, the first equation for the probability density function for the sales price of a home is found as follows. f(x) = 1/b – a, a ≤ x ≤ b = 1/230,000 − 200000, 200,000 ≤ x ≤ 230,000 = 1/30000, 200,000 ≤ x ≤ 230,000 Everywhere else, the probability density function will just be 0. Therefore, the full probability density function for the sales price of a home follows. f(x) = _______________ 200,000 ≤ x ≤ 230,000 elsewhereThe life X (in hours) of a battery in constant use is a random variable with exponential density. What is the probability that the battery will last more than 12 hours (h) if the average life is 8 h?
- Suppose X1, X2, X3 denote a random sample from the exponential distribution with density function. Please at the image for the full questions.A lamp has two light bulbs with an average lifespan of 1000 hours. Assuming we can model the probability of failure of these bulbs by an exponential density function with mean mu=1000, find the probability that both of the lamp's bulbs fail within 800 hours.For a continuous pdf, the probability of an exact value can be found . Is this true or false ?