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Using jacobian method finding the probability density function
Let X ~ Exponential (λ), for some constant λ > 0. That is,fX(x) = λ e-λx = λ exp( -λx ), x > 0, ( fX(x) = 0 otherwise)
(a) Create a transformed random variable Y = ln(X) (natural log of X). Using either the CDF method or Jacobian method, show that the probability density function of Y is given by:fY(y) = λ exp( y - λey ), -∞ ≤ y ≤ ∞.
(b) Verify that the CDF of Y is FY(y) = 1 - exp (-λey ), -∞ ≤ y ≤ ∞.
(c) If λ = 1, compute the median of Y.
The 95% confidence interval for the mean of the sampling distribution of the mean is about:
Iit is known that signal change in this brain area is normally distributed with mean of 35 and standard deviation of 10. By using .01 level, what must researcher conclude?
You will investigate four different scenarios of population growth also decline in this town. Graph the model as well as investigate it by four different growth models.
Explain the effect outliers can have on the analysis of the center of this data set. Based on the box-plot and histogram you created for problem 1, do there appear to be any outliers?
The Wilcoxon rank sum of the ranks for group and The value of the Wilcoxon signed rank statistic
Let X 1 , X 2 , X 3 , X 4 be a random sample from a Poisson distribution with parameter λ and let Y = X 1 + X 2 + X 3 + X 4 . You decide to test λ = 1.60 versus λ
For each problem, compute a Welch F-statistic and determine whether or not significant differences exist among the treatment conditions.
What is the likelihood the sample mean is greater than $22.50 but less than $25.00?
A certain airplane has 2 independent alternators to provide electrical power. The probability that a given alternator will fail on a 1 hour flight is 0.02. What is the probability that (a) both will fail? (b) Neither will fail? (c) One or the othe..
At the 5 percent level of significance, can we conclude that the mean weight is greater than 16 ounces? Determine the p- value.
Which of the given experiments can be modelled by Poisson distribution?
MATH1550H: Assignment:Questions: (Genetics) What is the probability that at most two of the offspring are aa?
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