The table below gives the joint probabilities distribution of two random variables X & Y Green (X=1) Red (> Apple (Y -0) 3/12 2/12
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- You own a company called Company X, which has monthly sales that are independent normal random variables with mean 100 and variance 10. Your rival company, called Company Y, has monthly sales that are independent normal random variables with mean 110 and variance 20. (a) Find the probability that your company, Company X, makes more than $307 this quarter (a quarter is 3 months). (b) What is the probability that your company makes more money than your rival company this month?If Xis a random variable having a binomial distributionwith n = 20 and p = 0.4, and Y is a transformed version of X,where Y = 2X + 3, what is the expected value of Y?A certain type of tree has seedlings randomly dispersed in a large area, with the mean density of seedlings being approximately three per square yard. If the seedlings are randomly dispersed, the number of seedlings per region, Y can be modelled as a Poisson random variable. If a 1 forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none of the regions will contain seedlings is 0.0498. 2.3.1 If the seedlings really are randomly dispersed, the number of seedlings per region, Y, can be modelled as a Poisson random variable with 2 = 3. Interpret 1 =3. 2.3.2 State the moment generating function_of the random variable Y.
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- The executives at a software company called Front Line are trying to decide if they should continue to provide free coffee in their breakrooms. They have 79 employees and each employee has a 67% chance of drinking coffee in the break room each day. Recall, for a binomial random variable, dbinom(j,n,p) = P(Y=j) and pbinom(j,n,p) = P(Y< j). What is the probability that more than 56 but at most 62 employees drink coffee in one day?3. Table 1 below shows the probability distribution of hurricanes that have made landfall in the Caribbean. The random variable, X, is the category of the hurricane. Category 1 is the weakest hurricane level while category 5 is the strongest. Table 1 x 1 2 3 4 5 P(X=x) 0.41 0.34 0.13 0.07 * a) Find the value of ‘*’. [1] b) Find the expected category of hurricane to make landfall, E(X). [2] c) What is the probability that a Category 4 or stronger hurricane will make landfall?[1] d) Calculate the variance. [3]