
Cov((T,N)=E(TN)-E(T)E(N)=E{NE(T|N)}-E(T)E(N)=E(N*700N)-1153.53*1.6479
=700*{V(N)+E2(N)}-1153.53*1.6479
=700*(.7427+1.6479*1.6479)-1153.53*1.6479=519.89
corr(T,N)=519.89/[SD(T)SD(N)]=519.89/square root of (561671*.7427)= 0.8049404
For query, comment.
4. Suppose that N is a random variable having a conditional Poisson distribution with ability mass...
3.14. Problem*. (Section 10.4) Suppose that for a Poisson random variable N, the param- eter is not constant, rather, it an exponential random variable with parameter 1. (a) Find an expression for P(N = j). (b) Compute the conditional probability that i < 1 given that N = 2.
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Please show your work! especially for part B
A Poisson distribution with λ=2 X~Pois(2)
A binomial distribution with n=10 and π=0.45.
X~binom(10,0.45)
Question 4. An inequality developed by Russian mathematician Chebyshev gives the minimum percentage of values in ANY sample that can be found within some number (k21) standard deviations from the mean. Let P be the percentage of values within k standard deviations of the mean value. Chebyshev's inequality states...
The number of customers arriving at a fast food restaurant are modelled on a Poisson random variable X with parameter A = 1. The total time that it takes to serve k customers, k> 1, is modelled on a continuous random variable T that is uniform in 0,k+ 1]. (a) (2 points) Compute the probability P(T 1 (b) (2 points) Compute the expected value of T
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chebyshev’s inequality
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