where c E R is a constant. a. Find the value of c that makes this function a valid probability density function. b. Find the cumulative distribution function, F(x), of X. c. What is the probability that more than 75% (0.75) of voters approve of the new proposal ?

Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let  denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.   a.  Select the probability density function.   1.     2.     3.     4.         b.  What is the probability of generating a random number between 0.15  and 0.85 (to 1 decimal place)?   c.  What is the probability of generating a random number with a value less than or equal to 0.3  (to 1 decimal place)?   d.  What is the probability of generating a random number with a value greater than 0.6  (to 1 decimal place)?   e. Using 50  random numbers given below, compute the mean and standard deviation.   0.467202 0.370629 0.966103 0.003795 0.877402 0.626396 0.816661 0.955063 0.569638 0.793645 0.641853 0.189704 0.519289 0.876775 0.016900 0.232961 0.807478…

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…

Let X be the number of visits to the dentist's office for a randomly selected student. Suppose that X has a probability distribution function given by the following table: X P(X= x) 0.15 0.65 Find P(X ≤u) where µ = E(X) is the average number of visits. 0.5 0.15 1 1 0.50 2 0.35