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- The probability distribution of a random variable x is as shown in the following table: x -2 1 5 6 P(x) 0.16 ? 0.31 0.21 a)Find P(x=1) b)Find the probability that the random variable x is at most 2. c)Find the probability that the random variable x is at least 1. d)Find P(0<x<1) e)Find P(2<x<6)K 2) d) Find the value of t and p if P(t t) : = 3) Suppose that X~x²(v) and Y~x²(n). If µx = 6, o²y = 16 and W a) State with parameter(s) the distribution of W. 4X 3Y Ơ V = thenLet X be the total number of groups of customers at Jellibabix's restaurant over one day in Lugdunum. Experience shows that X Poi(30). Each table (group of customers) orders at least one bottle of wine with probability p = 0.80. Suppose each table decides independently from other tables whether or not to order wine. If Y is the number of tables that ordered at least one bottle of wine, find the distribution of Y (hint: consider the distribution of Y given X = x).
- Let X be b(2, p) (binomial distribution). Assume P(X > 1) = (a) Find p. (b) Compute P[X = 2]. %3DPlease ASAP, answer all part or left it for other expertLet a function of random variable X is given by ( refer pictures) : a) Find the value of K b) Form the table of probability distribution of X C) Find the mean and variance of the distribution
- Q6The profits of a mobile company are normally distributed with Mean of R.O (17x 10) and standarddeviation of R.O (17).a. Find the probability that a randomly selected mobile has a profit greater than R.O ((17x10) +10)A discrete random variable x has the the following probability distribution X 2 3 4 5 6 P(X=x) 3k2k2 3k2k2 3kk 2kk kk i) Find the value of k? ii) Find P[X>5][3.5<X<6.5]P[X>5][3.5<X<6.5]
- Q8 and Q9 pleaseLet X be a discrete random variable with PGF P(s) = a. Find the probability distribution of X. b. Derive the mean and variance of X using its PGF.Consider a probability space (2, F, P) and a random variable X defined on it. Recall the definition of the distribution ux. Show that the distribution defines a probability on B.