Given that X is a random variable having a Poisson(λ) distribution, compute the following: P(X<8)when λ=6 P(X<8)=

The continuous random variable X has a U (-6, 6) distribution, i.e. uniformly distributed between the points a = -6 and b = 6.  What is the mean of X, and what is P (-3 < X < 1)?

We are trying whether, a new low fat diet actually helps obese people lose weight. 100 randomly obese people are assigned to group 1 and put on a low fat-diet. another 100 people are assigned to group 2 and put on a diet of approximately the same amount of food, but not as low in fat. After 4 months, the mean net weight loss was 9.31 pounds for group 1 with a standard deviation of 4.67 pounds, and for group 2 the mean net weight loss was 7.40 pounds with a standard deviation of 4.04 pounds. Is the low-fat diet more effective? Perform a hypothesis test at the 5% significance level a) Define Parameters and state null and alternative hypothesis b) Find test statistics c) Find p-value d) Conclusion

Suppose (S, P) is a binomial distribution with n trials and probability of success p. Let X be the random variable X(k) = k³, where k is the number of successes. Calculate E[X].