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- Q1. Let x be a random variable with density function 2 (k+1)x 0 < x < 1 0 otherwise 9 = f(x): Find the moment generating function of x.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%?1. Let X be a continuous random variable with the following density function: cx,01.The probability density function of a continuous random variable X is given by f(x) : 04 i) Find k ii) Find P (1.5SHOW ONLY THE SET-UP FORMULA AND GRAPH ITThe joint probability density function of X and Y is defined as f(r, y) = (1+2?)(1+y²) What is the probability that (X, Y) falls inside the square with vertices (0,0), (1,0), (1,1), and (0,1)? 16 O 1/2 O None of these. O 1/16None1) Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the estimator of moments for the parameter θ.The probability density function of X is given by X 1 3 4 5 6 P(X) K 3K 5K 7K 9K 11K 13K Find (i) P (X 5) (iii) P (3 0.3.An organization for people with high IQ, and eligibility requires an IQ above 131.5. Suppose the IQ scores are normally distributed with a mean of 102.5 and standard deviation of 16.1. If someone wants to join the organization, what is the probability that he or she meets the organization’s requirement?E The density function of a continuous Random variable X is fx (x) = ax 0 Sx <1 for for 1|f(x)dx = 1 Find the 2 Let x be a continuous random variable over [a,b] with probability density function f. Then the median of the x-values is that number m such that a median. 1 f(x) = 50 x, [0,10] ... The median is m=Recommended 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