Imagine that people enter a room one by one and announce their birthdays. Let the random variable X be the number of people required to have a matching birthday. What is the probability mass function of X?

Box Aand Box B contain 1, 2, 3, 4. Write the probability mass function and draw the histogram of the sum when one number from each box is taken at a time, with replacemen

Let random variable X denote the length of a wire, assumed to be exponentially distributed with mean 107 cm. The wire is cut to make rings of radius 1 cm. Derive the probability mass function for the number of complete rings that can be produced by each length of wire.

Assume that the machine yields the item selected 90 percent of the time, and returns nothing 10 percent of the time. Three individuals attempt to use the machine. Let X be defined as the number of individuals who obtain the item selected. How many different values are possible for the random variable X? Fill in the table below to complete the probability density function. Be certain to list the values of X in ascending order.

Assume that when adults with smartphones are randomly selected, 53% use them in meetings or classes. If 10 adult smartphone users are randomly selected, find the probability that at least 3 of them use their smartphones in meetings or classes. The probability is 0.0905 (Round to four decimal places as needed.)

a box contains 6 balls, 4 of which are red. I randomly select 3 balls from the box. Find the probability mass function of getting 2 red balls?