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- The probability density function of X, the lifetime of a certain type of device (measured in months), is given by if x 24 Find the following: P(X > 40) = The cumulative distribution function of X: if a 24 The probability that at least one out of 6 devices of this type will function for at least 46 months:Probability.1 Find the probabilities that the length of a randomly selected petal will be as 2/x The length of a petal on a certain flower varies from 2.56 cm to 6.76 cm and has a probability density function defined by f(x) = follows. a. Greater than or equal to 3.4 cm b. Less than or equal to 3 cm c. Between 3 cm and 3.4 cm
- 5 A new dairy product is tested extensively to determine its shelf life in days. The measure- ments can be modelled by the following probability density function. t/72 0Suppose you have the probability density function if 3 < x < 9 f(x) otherwise Find the cumulative distribution function of X. Select an answer ♥ F(x) if Select an answer if Select an answer Note: When writing your piecewise function, start with the left-most interval.For what value of c is the function f(x) = {c/x³ if x ≥ 1 {gx3 otherwise a probability density function?Let X₁, X₂, X3,..., Xn denote a random sample of size n from the population distributed with the following probability density function: f) f(x; 0): = {CO.. ((0+1)xº, if 0A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on their experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = = {₁x2²; 0 (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X. (d) Use Tscheby schev's inequality to determine the probability that X does not deviate more than 0.5 from its expectation.The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…Verify Property 2 of the definition of a probability density function over the given interval. 1 10 f(x)= [4,6]2..You are given fT(30)(t) = t/1250 0≤t<50 0 o.w. a) Find the probability that (30) dies between ages 40 and 45. b) Find the probability that (60) dies between ages 65 and 85. c) Define the cumulative distribution function of T (45). d) Define the force of mortality of T (50).[1] The probability density function of a random variable X is SC(x + 4), -4 4.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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