A consignment of 7 refrigerator sets contains 5 sets with no scratch on them. A hotel makes a random purchase of 3 of the sets. If X is the number of refrigerator sets purchased with a scratch on it, a) Find the probability distribution of X. b) Find the Cumulative Distribution Function (CDF) of X. c) Construct a graph of the CDF.

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A consignment of 7 refrigerator sets contains 5 sets with no scratch on them. A hotel makes a random purchase of 3 of the sets. If X is the number of refrigerator sets purchased with a scratch on it, a) Find the probability distribution of X. b) Find the Cumulative Distribution Function (CDF) of X. c) Construct a graph of the CDF. d) Using CDF, find P(0<X≤2) ii) a) Suppose Let X denote the proportion of time in a day that a randomly selected student spends on a smart phone. Suppose the probability density function of X is ??(??;??)= �(??+1)???? 0≤??≤1, −1<?? 0, ??????????ℎ?????? A random sample of 5 students is taken with the following observation, 0.34, 0.40, 0.12, 0.55 and 0.01. Use the method of moments to obtain an estimator of ?? and then compute the estimate of this data

b) If U and V are two independent standard normal random variables and Z=0.6U+0.8V. Determine Corr (U , Z) iii) On the basis of a survey of 25 random typists, a confidence interval for the mean time needed to complete typing a page was (5.588; 6.412). Knowing that the distribution of the time needed to type a page is normal, and the sample standard deviation was equal to 1, determine the confidence level used for the calculations.

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