The price of a stock on a given trading day changes according to the distribution 0...

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The price of a stock on a given trading day changes according to the distribution 0 1 ")- 1/4 1/2 1/8 1/8) 2 Px (a) Manually find the distribution for the change in stock price after three independent trading days. More specifically, let (X1, X2 , X3 ) be the individual changes in stock price after three trading days. find the probability distribution of T= X, + X2 + X3 . (b) Refer to the lecture notes. Use R function conv(x, px, y, py) to determine, using the concept of convolution, the desired distribution in (a). Don't forget to install the R package kSamples before you use the conv() function. See the demo R code in the lecture notes of 10/19. Use R to simulate the distribution of T in Problem 7 part (a). Compare the simulated probability mass function and the theoretical probability mass function. The price of a stock on a given trading day changes according to the distribution 0 1 ")- 1/4 1/2 1/8 1/8) 2 Px (a) Manually find the distribution for the change in stock price after three independent trading days. More specifically, let (X1, X2 , X3 ) be the individual changes in stock price after three trading days. find the probability distribution of T= X, + X2 + X3 . (b) Refer to the lecture notes. Use R function conv(x, px, y, py) to determine, using the concept of convolution, the desired distribution in (a). Don't forget to install the R package kSamples before you use the conv() function. See the demo R code in the lecture notes of 10/19. Use R to simulate the distribution of T in Problem 7 part (a). Compare the simulated probability mass function and the theoretical probability mass function.

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