1. KKS Company offers special decorated cakes for birthdays, weddings, and other occa- sions. The following...

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1. KKS Company offers special decorated cakes for birthdays, weddings, and other occa- sions. The following table gives the total number of cakes demand per day, X, and the following probability mass function. x 10 11 12 13 14 15 P(X = x) 0.28 0.42 0.12 0.08 0.07 0.03 (i) What is the probability that at most 12 cakes are demanded in one particular day? (ii) Write down the cumulative distribution function of X. (iii) What is the mean and standard deviation of X? (iv) If KKS Company decides to bake only 13 cakes in each day, it will makes a profit of $20 for each cake sold and a loss of $8 for each unsold cake. Let Y be the net amount of total profit made by selling the cakes in one day. Write down the probability mass function of Y. (v) What is the probability that the company sells exactly 11 cakes in each of five days within a particular week? Assume that the numbers of cakes sold in each day are independent. 1. KKS Company offers special decorated cakes for birthdays, weddings, and other occa- sions. The following table gives the total number of cakes demand per day, X, and the following probability mass function. x 10 11 12 13 14 15 P(X = x) 0.28 0.42 0.12 0.08 0.07 0.03 (i) What is the probability that at most 12 cakes are demanded in one particular day? (ii) Write down the cumulative distribution function of X. (iii) What is the mean and standard deviation of X? (iv) If KKS Company decides to bake only 13 cakes in each day, it will makes a profit of $20 for each cake sold and a loss of $8 for each unsold cake. Let Y be the net amount of total profit made by selling the cakes in one day. Write down the probability mass function of Y. (v) What is the probability that the company sells exactly 11 cakes in each of five days within a particular week? Assume that the numbers of cakes sold in each day are independent.