Show that if ν > 2, the chi-square distribution has arelative maximum at x = ν − 2. What happens whenν = 2 or 0 <ν< 2?
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Show that if ν > 2, the chi-square distribution has a
relative maximum at x = ν − 2. What happens when
ν = 2 or 0 <ν< 2?
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- solve it correctly. i will rate6. The probability density function of (lifetime of an electronic component in years) X is fx (x) = A xexp U (x) 32 (a) What value of A will make this a valid pdf? (b) What is the probability that it will fail within 6 years, given that normally these units tend to fail within 4 to7 years? (c) What is P[|X-3|<6]? (d) If the unit is known to fail within 6-8 years, what is the probability that it fails within 7 years.10. It is known that the probability of being able to log on to a computer from a re- mote terminal at any given time is .7. Let X denote the number of attempts that must be made to gain access to the computer. (a) Find the first four terms of the density table. (b) Find a closed-form expression for f(x). (c) Find P[X = 6]. (d) Find a closed-form expression for F(x). (e) Use F to find the probability that at most four attempts must be made to gain access to the computer.
- 1. X is a normally distributed variable with mean μ = 30 and standard deviation o = 4. Find a) P(x 21) c) P(304. Show that for the exponential distribution -x/0 dP = yo e dx, 0Please do not give solution in image formate thanku. 16. Let Q1 be the lower and Q2 the upper end point of the 96 percent confidenceinterval for the sample proportion ˆp if the success count in the sample is x = 512 andn = 698 is the sample size. Let Q = ln(3 + |Q1| + 2|Q2|). Then T = 5 sin2(100Q)satisfies:— (A) 0 ≤ T < 1. — (B) 1 ≤ T < 2. — (C) 2 ≤ T < 3. — (D) 3 ≤ T < 4. — 4 ≤ T ≤ 59. Let X and Y be independent exponentially distributed RVs with parameters A and B, respectively. Use the MGF approach to find the CDF and the PDF of Z = X+Y. E [e=²(*^_^₂)] = E [e³*] E[e³r] *M(s) XAY = M₁ (3) My (1) = (-_^) ( P-²) =2. Find the critical value using the Chi-Square Table for a = 0.10, n = 7, two- tailed.Show that a gamma distribution with α > 1 has a rel-ative maximum at x = β(α − 1). What happens when 0 <α< 1 and when α = 1?2. In probability, it is common to model the deviation of a day's temperature from the monthly average temperature using the Gaussian probability density function, 1.-/9 f(t) = V9T This means that the probability that the day's temperature will be between t = a and t = b different from the monthly average temperature is given by the area under the graph of y = f(t) between t a andt = b. A related function is %3D F(x) = -2/9 dt, 2 0. %3D V9n Jo This function gives the probability that the day's temperature is between t = -x and t = x different from the monthly average temperature. For example, F(1) 0.36 indicates that there's roughly a 36% chance that the day's temperature will be within 1 degree (between 1 degree less and 1 degree more) of the monthly average. 1 (a) Find a power series representation of F(x) (write down the power series using sigma notation). (b) Use your answer to (a) to find a series equal to the probability that the day's temperature will be within 2 degrees of the…Please help solve this14. Show that for the Gamma distribution e dp = dx, 0SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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