f(x) = = 0.475 0 0.075x 0.075.x for 1 ≤ x ≤ 5 elsewhere The probablity density function for continuous random variable, x, is given above. Find P(x<3)
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- please solve all partsLet X-N(2,5). Let f be the density of this random variable. We want to evaluate in R f(6). Which of the following statements are true? The normal distribution N(2, 5) 0.08 - 0.06- 0.04 - 0.02 - 0.00 -10 10 The answer is The R instruction is dnorm(-2,2,5) Can you explain why ? Density f(x)The probability density function for a continuous random variable X is given by 0 < x < 1 1≤ x ≤ 2 else Find P(0.5 < X < 1.5) Round to 4 decimal places if needed. f(x) = X 2-x
- Continuous random variables 6. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Find the Expected value and Standard deviation.Express your answer in 3 decimal place value f(x)= - c(x-1)(4-x) 0 for 1A continuous random variable X has density given by: f(x)= {1/2, -0.5≤x<0.5 {1, 0.5≤x≤1 {0 Based on this information, answer each alternative. a. P(X< −0.39 or X≥0.74): b. P(X≥−0.01): c. P(0.34≤X≤0.79): d. P(X≥0.36|X≤0.99): e. P(X≤0.63|X≥0.31):The continuous random variable, X, has the probablity density function given below. n* f(x) = for 0 < x < 10 20 elsewhere P(x < 0.5) =|The random variable X has expected value E(X)=4 and Var(X)=4. Here, we want to approximate the probability that X lies in the interval [3.4,5.4] using a transformation to a standard normal distribution Z. Then we will need to calculate the probability that Z lies in the interval [z1,z2] where z1= z2= Suggest z1 and z2 Do NOT attempt to make any sort of continuity correction.The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8Continuous random variables 5. A charity group raises funds by collecting waste paper. A skip-full will contain an amount, X of other materials such as plastic bags and rubber bands. X may be regarded as a random varibales with probability density funnction. All nmerical values are in units of 100kg. Calculate c. express your answer in fraction c(x - 1)(4x) f(x) = _{[C(x − 1) for 1Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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