Express the tossing of one coin as a probability distribution of x, the number of heads occurring (that is, x = 1 if a head occurs and X = 0 if a tail occurs). (Give your answers correct to one decimal place.) no) = :1 rm = :1 Test the following function to determine whether it is a probability function. If it is not, then make it into a probability function. (Give your answers correct to one decimal place.) R(x) = 0.2, for X = 0, 1, 2, 3, 4 (a) List the distribution of probabilities. R(O) = lllll Test the following function to determine whether it is a probability function. (Give your answers correct to two decimal places.) 2 P(X) = X5; 5,forx= 1,2, 3,4 (a) List the probability distribution. Pu) = :1 Pa) = :1 P8) = :1 PM) = :1 Census data are often used to obtain probability distributions for various random variables. Census data for families in a particular state with a combined income of $50,000 or more show that 15% of these families have no children, 29% have one child, 25% have two children, and 31% have three children. From this information, construct the probability distribution for x, where x represents the number of children per family for this income group. (Give your answers correct to two decimal places.) P(0 children) = : P(1 child) = : P(2 children) = :l P(3 children) = :l Consider the probability function. (Give your answers exactly.) P(x)= 5'X, forX= 1, 2, 3,4 10 (a) Find the mean. :] (b) Find the standard deviation. l:l Consider the probability function. (Give your answers correct to two decimal places.) R(X) = 0.2, for x = 0, 1, 2, 3, 4 (a) Find the mean. :l (b) Find the standard deviation. l:l The number of ships to arrive at a harbor on any given day is a random variable represented by X. The probability distribution ofx is as follows. (Give your answers correct to two decimal places.) x l 10 11 12 13 14 P(X) loss 0.13 0.15 0.15 0.19 (3) Find the mean of the number of ships that arrive at a harbor on a given day. S (b) Find the standard deviation, 0, of the number of ships that arrive at a harbor on a given day. S