The cumulative distribution function F(x) of a random variable X is given by 0, -8
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- Draw all possible samples each of size 2 from the population 2, 4, 6 and 8 using sampling with replacement. Find mean of each sample and verify that (6) Mean of = u and (ii) V(X) (ii) V(R) %3DX is a Uniform(8, 20) random variable what is Var(X)=?A random variable has poisson distribution such that P (X = 3) = P (X= 4). Find p (6).
- Suppose a random variable X has the following pdf. The random variable X has a Beta distribution with α = 3 and β = 2. Suppose we wanted to determine Var( 10X - 3 ). By the rules for variances, Var( 10X - 3 ) = * Var(X) + where, using the fact that X has a Beta distribution, Var(X) = Express answer as a decimal. Do not round.(13) Let X b(6,-) find E(5+6x) and distribution function. 3A random point (X,Y) is distributed uniformly on the square with vertices (1,1), on the square. (1,-1), (-1, 1), and (-1,-1). That is, the joint pdf is f(x,y) Determine the probabilities of the following events. (a) x² + y² 0 (c) |X+Y| < 2
- A random variable X has the distribution B(12, p). (a) Given that p = 0.25 find (i) P(X 7)Suppose that a medical test has a 85% chance of detecting a disease if the person has it (P(PT|D)=0.85) and a 90% chance of correctly indicating that the disease is absent if the person really does not have the disease (P(NT|Dc=0.90). Suppose that 95% of the population does not have the disease P(Dc)=0.95 What is the probability that a randomly chosen person will test negative P(NT)?Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)
- Weights (X) of men in a certain age group have a normal distribution with mean μ = 150 pounds and standard deviation σ= 28 pounds. Find each of the following probabilities. (Round all answers to four decimal places.)(a) P(X ≤ 136) = probability the weight of a randomly selected man is less than or equal to 136 pounds.(b) P(X > 136) = probability the weight of a randomly selected man is more than 136 pounds.I have a probability distribution consisting of (x, p(x)): (-3, 0.1), (-2, 0.2), (-1, 0.3), (0, 0.05). The probabilities obviously do not sum to 1. How do I find <x> (average), <x2> (the second moment), <sigmax2> (the variance)?