Problem 11.6. Source: Sample STAM problem #179. The time to an accident follows an exponential distribution. A random sample of size two has a mean time of 4. Let Y denote the average of a new sample of size two from the same distribution. Calculate the maximum likelihood estimate of P[Y>8]. Hint: Remember that the sum of independent, identically distributed exponential random variables has a gamma distribution. You can convince yourselves of this fact using moment generating functions.

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A: The first derivative of moment generating function is, The mean of the distribution will be: Thus,…

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

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A: From the above given data the following solution is provided below:

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Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

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A: True

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Q: (a) (b) What is E[V]? What is Var[V]? (c) What is EV³ ]?

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Q: 3. Aggregate risk S comes from compound Poisson random variable with N- P(100) and individual claims…

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Q: 4. The Poisson distribution is an important discrete distribution used to model events that occur…

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Q: (a) Karl Pearson's coefficient of skewness for a distribution is - 0.4, its mean is 50 and…

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Q: Suppose random variable X has probability distribution Ax) = (x² +4)/30 for x = 0, 1, 2, 3. Fifty…

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Q: Problem 4. Let X1, X2, . .. be i.i.d. random variables. Each X; follows Exponential (A) with the =…

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Q: Use Poisson Distribution to solve problem 4 4. Complaints about an Internet brokerage firm occur at…

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Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x =0 (ii) 1Sx<4 eor…

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Q: 4. In a Exponential distribution with a λ of 5 defects per one square yard, the probability of…

A: Given data  λ = 5 defects per square yard x = no. of defects per square yard P(x&lt;6) = ?

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Q: Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per…

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Q: If all possible samples of size 16 are drawn from a nearly normal population with mean equal to 30…

A: From the provided information, Mean (µ) = 30 Standard deviation (σ) = 6 X~N (30, 6)

Q: 6. Show that 1 s2 = TE2-1(Xi – x)² is unbiased estimator of the population variance o?

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Q: Example 9-4. X is a normal variate with mean 30 and S.D. 5. Find the probabilities (i) 26 5.

A: We have given that.   X~N( μ , ?^2 )   μ =30 , ? =5   Z-score =( x - μ )/?