After an analysis conducted by the market intelligence department of a chemical importing company, it was concluded that

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After An Analysis Conducted By The Market Intelligence Department Of A Chemical Importing Company It Was Concluded That 1 (127.1 KiB) Viewed 74 times

After an analysis conducted by the market intelligence department of a chemical importing company, it was concluded that there will be an increase in the demand for TDI (toluene diisocyanate) in the Colombian market. Due to the company's company policies, only sales of 60, 80, 100 and 120 tons of the chemical will be made in the next 6 months. tons of the aforementioned chemical in the next 6 months. It is estimated that the number of tons that will be sold in the next month can be modeled by the random variable X with the following function X with the following probability function: x 0 9x(x) k 60 80 100 0.1 C 0.42 120 0.21 In addition, it has been estimated that at least 60 tons of TDI will be sold per month with a probability of 0.98. a. Find the values of cand k so that gx(xi) is a well-defined probability function. b. Find the Cumulative Distribution Function, Fx(x), of the random variable and graph it. c. Find the expected value of the random variable X and interpret it. d. The company's monthly profits, in millions of pesos, according to the number of tons sold, can be expressed by the variable Y the number of tons sold, can be expressed through the variable y defined as: Y = VX +0.9X + 10. Calculate the expected value of the company's monthly profits and interpret this result. e. Find the variance of the random variable X. f. Find the standard deviation of the random variable and interpret your result.