3 The table below gives the probability distribution of X = number of ear infections for children during the winter. (5 points each) Value ofX 0 1 2 3 4 5 Probability 0.10 0.10 ????? .35 .16 .05 (3) Find x = 2). (Hint: What must the sum of all the probabilities in the samples space equal?) 2 P(X)=1 | 0.10+0.10+P(x=2) +0.35+0.16+0.05= 1 0.10+0.10+0.35+0.16+0.05= 0.76 P(x=2) +0.76=1 P(x=2) = 0.24 (b) Find the probability that a randomly selected child had 3 or more ear infections during the winter. (0) Find the probability that a randomly selected individual had 3 or 5 ear infections. (d) Find the cumulative probability x 5 2). 4. Again using the scenario above in question 3, calculate the g5 points each) (8) )Expected value of the random variable X (X = number of ear infections for a child during the winter) (b) Find the standard deviation of the random variable X (X = number of ear infections for a child during the winter in a large population)