A continuous random variable X that can assume value between x-2 and x-5 has a density function given by 1+x f(x) = 8 a. Show that P(2
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- 3. Let X be a scalar random sample from the following density f(x) = 2(0-x) 82 Construct a (1-a) Cl for 0. for 0 ≤ x ≤ 0Let X be a continuous random variable with density function fx(x) ((3/2)x?) 1-1.1(X). Find the density function of W=2-X, using the CDF technique.A continuous random variable that can assume values between X = 2 and X 5 has a density function given by fx (x) = K (I +x). Find p (3 < X < 4)
- Moulinex is a well-known brand on the market that produces blenders. The time needed to produce one blender is expressed in minutes and can be modelled as a continuous random variable X with density function f(x) = {a ·⋅ (x − 53) · (57 − x)³ 0 if 53 ≤ x ≤ 57, otherwise You may assume that the production times for producing different blenders are independent of each other. C. a. Show that a = 1 / 51.2. b. Determine the median production time and the mode of the production time of the blenders of the brand Moulinex. Determine the probability that the total production time needed to produce 50 blenders exceeds 45 hours. d. What is the maximum number of blenders that can be produced with a total production time of at most 40 hours with a probability of at least 95%?The joint density function of two continuous random variables X and Y is fxy(x, y) = (2x+y) if 2Let X be the proportion of new restaurants in a given year that make a profit during their first year of operation, and suppose that the density function for X is ƒ(x) = 20x³(1 − x) Find the expected value and variance for this random variable. E(X) = = Var(X) 0 ≤ x ≤ 1Determine the conditional probability distribution of Y given that X = 2. Where the joint probability density function is given by f(x,y)= 1 - (x + y) for 1 < x < 4 and 0 < y < 3.Please solve this question in probability and statisticsConsider the probability density fx (x) = a. eb x! where X is random variable whose allowable values range from x = -o to + o. Find (a) the CDF (b) the relation between a and b (c) the probability that x lies between 1 and 2.Let x be a random variable with a density function I (2) = { "0, 6x (1 – a), 0 < x < 1 elsewhere By finding the fırst and second moments, calculate the variance of x [1] (answer correct to 1 dp)The random variable X has the density function: x) = (2-x). 0sxs1 f(x) = (a) The standard deviation of X is |. (Round to four decimal places including any zeros.) (b) According to the Chebyshev's theorem, for k= 1.78, the probability P ORecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON