1. Julia and Tony play the hand game rock-paper-scissors. Assume that, at each play, they make...

 

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1. Julia and Tony play the hand game rock-paper-scissors. Assume that, at each play, they make their choices with equal probability ) for cach of the three moves, independently of any previous play. a) On any single play, what is the chance of a tie? b) What is the chance that Julia wins at the first play? Let Random variable X- rock The probability distribution is shown below 1 4 frequency f P(X) 4 4 c) Find P(X = 1) d) Find P(X 2 1) %3D 2. Consider again the example of the number of languages spoken by Filipino school children. Define X to be the number of languages in which a randomly chosen Filipino child attending school can hold an everyday conversation. Assume that the probability function of X, P(x), is as shown in the following table. 1 2 3 4 6. P(x) 0.663 0.226 0.066 0.022 0.019 0.004 a. What is the mean of X? b. Find the variance of X c. Find the standard deviation of X. 2119 419 1. Julia and Tony play the hand game rock-paper-scissors. Assume that, at each play, they make their choices with equal probability ) for cach of the three moves, independently of any previous play. a) On any single play, what is the chance of a tie? b) What is the chance that Julia wins at the first play? Let Random variable X- rock The probability distribution is shown below 1 4 frequency f P(X) 4 4 c) Find P(X = 1) d) Find P(X 2 1) %3D 2. Consider again the example of the number of languages spoken by Filipino school children. Define X to be the number of languages in which a randomly chosen Filipino child attending school can hold an everyday conversation. Assume that the probability function of X, P(x), is as shown in the following table. 1 2 3 4 6. P(x) 0.663 0.226 0.066 0.022 0.019 0.004 a. What is the mean of X? b. Find the variance of X c. Find the standard deviation of X. 2119 419