The number of defaults in one year within a certain portfolio of bonds is found to...
The number of defaults in one year within a certain portfolio of bonds is found to be a Poisson random variable with parameter λ = 7 (i.e., the portfolio has an expectation of 7 defaults per year).
(a) Find the probability that the bond portfolio will have fewer than 3 defaults during the upcoming year.
(b) Describe the distribution of the continuous random variable representing the time between successive defaults.
(c) Find the expected time between successive defaults.
(d) Calculate the probability of there being less than 6 months between two successive defaults
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The number of defaults in one year within a certain portfolio of
bonds is found to...
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5. Suppose that the number of accidents on a certain motorway each day is a Poisson random variable with parameter (mean rate) A-3. (i) Find the probability that there are more than three accidents today. (ii) Repeat (i), given that at least one accident occurs today
Hello, need help solving the rest. I might be doing it wrong and cannot figure it...
Hello, need help solving the rest. I might be doing it wrong
and cannot figure it out. Thank you.
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Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability...
Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is r E 0,1,2,...) This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a) Prove by direct computation that the mean of...
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need to check my work. Just need B and C Problem 2. Recall that a discrete...
need to check my work. Just
need B and C
Problem 2. Recall that a discrete random variable X has Poisson distribution with parameter λ if the probability mass function of X is fx (x) = e-λ- XE(0, 1,2, ) ar! This distribution is often used to model the number of events which will occur in a given time span, given that λ such events occur on average a Prove by direct cornputation that the mean of a Poisson randoln...
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(3.4) This question is about a continuous probability dis- tribution known as the exponential distribution Let x be a continuous random variable that can take any value x 20. A quantity is said to be exponen- tially distributed if it takes values between r and r + dr with probability where A and A are constants. (a) Find the value of A that makes P() a well- defined continuous probability distribution so that Jo o P(x) dx = 1 (b)...
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Hello, need help solving the rest. I might be doing it wrong
and cannot figure it out. Thank you.
The Poisson distribution gives the probability for the number of occurrences for a "rare" event. Now, let x be a random variable that represents the waiting time between rare events. Using some mathematics, it can be shown that x has an exponential distribution. Let be a random variable and let o be a constant. Thenis a curve representing the exponential distribution....
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Recall that a discrete random variable X has Poisson
distribution with parameter λ if the probability mass function of
X
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need to check my work. Just
need B and C
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