I have the following 5 problems, please help me.
1.Let X have a Poisson distribution with parameter m. Show that
P(X is even)=(1+e2m)/2
2. A point is chosen at random on a circle of radius a, compute the mathematical expectation of its distance from a fixed point which is also on the circle.
3. Five balls are drawn at random from an urn containing 4 white and 6 black balls. Find the probability distribution of the number of white balls drawn when the balls are drawn with replacement.
4. A card is drawn at random from each of two well shuffled packs of cards. What is the probability that at least one of them is queen of spade.
5. Using Poisson distribution, find the probability that the ace of spade will be drawn from a pack of well shuffled cards at least once in 104 consecutive trials.
1.Let X have a Poisson distribution with parameter m. Show that
P(X is even)=(1+e2m)/2
2. A point is chosen at random on a circle of radius a, compute the mathematical expectation of its distance from a fixed point which is also on the circle.
3. Five balls are drawn at random from an urn containing 4 white and 6 black balls. Find the probability distribution of the number of white balls drawn when the balls are drawn with replacement.
4. A card is drawn at random from each of two well shuffled packs of cards. What is the probability that at least one of them is queen of spade.
5. Using Poisson distribution, find the probability that the ace of spade will be drawn from a pack of well shuffled cards at least once in 104 consecutive trials.