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- What does normalization mean in Bayes' Theorem?Let X be a continuous random variable with mean μ and standard deviation σ. If X is transformed to Y = 2X + 3, what are the mean and standard deviation of Y?Show that a random sample (X1,Y1),….,(Xn,Yn) from Bivariate normal distribution with is in the exponential family showing all calculation steps.
- Find the total of the areas under the standard normal curve to the left of z1=−2.575z1=−2.575 and to the right of z2=2.575z2=2.575.The table below shows a sample of waiting times (in days) for a heart transplant for two age groups. At α=0.05, can you conclude that the variances of the waiting times differ between the two agegroups?The table below shows a sample of waiting times (in days) for a heart transplant for two age groups. At α=0.05, can you conclude that the variances of the waiting times differ between the two age groups?
- 3. The probability of successfully navigating an asteroid field in a science fiction movie is found to be 0.01. A total of2000 spaceships attempt to navigate the field, and the number that make it through is recorded. Can thisdistribution be modelled using a normal approximation?X and Y be standard normal random variables with correlation ρ. Compute the joint and marginal distributions of X + Y and X-Y . Are X + Y and X-Y independent?How to get area between z and a z in a normal curve? specifically