# Question: A nonnegative random variable X has moments which are known

A nonnegative random variable X has moments which are known to be E [X] = 1 , E [X2] = 2 , E [X3] = 5 , E [X4] = 9 , E [X5] = 14 , E [X6] = 33. (a) Show that for any nonnegative random variable,

(a) Show that for any nonnegative random variable,

(b) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ≥2).

(c) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ≥ 3).

(a) Show that for any nonnegative random variable,

(b) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ≥2).

(c) Using the result of part (a) and the values of the moments given, find the tightest bound on Pr (X ≥ 3).

## Answer to relevant Questions

Since the Q- function represents the tail probability of a Gaussian random variable, we can use the various bounds on tail probabilities to produce bounds on the Q- function. (a) Use Markov’s inequality to produce an ...Suppose a fair coin is flipped n times and the random variable Y counts the number of times heads occurs. What is the entropy of Y in bits? Compare your answer to that of Exercise 4.85 and explain any difference. Use the characteristic function (or the moment- generating function or the probability-generating function) to show that a Poisson PMF is the limit of a binomial PMF with n approaching infinity and p approaching zero in such ...Suppose X is a random variable whose n th moment is gn , n = 1,2, 3.… In terms of the gn, find an expression for the m th moment of the random variable Y= aX+ b for constants a and b . A random variable X has a uniform distribution over the interval (– a / 2, a / 2) for some positive constant a. (a) Find the coefficient of skewness for X; (b) Find the coefficient of kurtosis for X; (c) Compare the ...Post your question