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Determine the
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- Consider two probability density functions: Select one: A. Data set A: 9₁ B. Data set A: f, Data set B: f OC. Data set A: g, Data set B: f Data set B: g For each of the following two observed data sets, which of the two density functions is more likely to be the true density of the data? • Data set A: {-0.7, 0.5, 0.2} Data set B: {-0.4,-0.2, 0.2, 0.4} D. O E. Data set A: f, Data set B: g The two densities are indifferent to both data sets f(x) = { 1 ² ₁ x, for 1Verify that the function corresponding to the following figure is a valid probability density function. Then find the following probabilities:Suppose that random variable X is uniformly distributed between 5 and 22. Draw a graph of the density function, and then use it to help find the following probabilities:Let X be the number of bathrooms in a randomly selected house for sale in Malibu, California. Suppose X has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution function. x 1 2 3 4 5 6 p(x) .05 .20 .32 .27 .10 .06 F(x) .05 .25 .57 a .94 1 a. What is the value of a? b. Calculate the probability that X < 3. c. Calculate the expected value of X. d. Calculate the variance of X. e. Calculate the expected value of x0.37 <_>f. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that each of the 3 selected houses has exactly 3 bathrooms? g. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that exactly two of the selected houses have exactly 2 bathrooms ? h. Malibu has a water crisis. The town board will solve this crisis by charging a special…In a probability density function such as a Normal or bell-shaped curve, the area under the curve is used to make predictions about likelihoods and probabilities. What is the area (use a proportion) under the curve from the lowest possible value to the highest possible value?Find the mean and variance of X given the following probability density function:Three 3-sided dice are tossed. Each die has its sides labeled 0, 1, and 2. Let X denote the product of the outcomes of the threee dice. Determine the probability mass function (pmf) of X.Let X be the discrete random variable with the following probability mass function: 0 1 2 3 0.5 0.3 0.1 0.1 f(x) Find the value of the cumulative distribution function F(2).Let x be the cost ($) of an appetizer and y be the cost of a main course at a certain restaurant for a customer who orders both courses. Suppose that x and y have the following joint distribution: X 5 6 7 Find the probability mass function of x. Find the probability mass function of y. 10 .20 .10 .10 y 15 .15 .15 .10 20 .05 .10 .05
