Question

Assignment 2 - Find 1. Suppose X has a discrete uniform distribution: PX - the distribution function of F ather Prethol FC) is the distributive function of any 3. The specifetime x in years of my powered b y J6), 35:56 (1) Find the value of Find the cliente functie X: G) Find the probability to the watch has sepert i 4 pr i me in (1) Find the conditional polyth the watches eroes of you that the watch has an opera r me 4. Suppose that and ter 2. Penethu variables -1 the expe a wiem i 1) ( 5. Let Xhea Binomial random variable with probability distribution Find the probability distribution of the random variable Y-X 6 Asmehalthe density function of random a lexis OSES Observe X repeatedly for times and let det he r the device values are larger than Find the distribut o 7. The functie for con sex X ) (P-1 X<1): the distribution functie :3the defence SI 21 Find (DP-1<x<2): the function of 9. A manufacturer of televisi o us that the wenge of this products are defective what is the probability that 1000 television produced will contain at least defectives

Answer 1

1 distribution x has a P(XER) discrete uniform I , 1=1,2... " if 220 F(X) = 1k -slxo k=1,2...n-1 1 ΠΕ Ocak α λη 2) F(x) = { Sinx OSxen otherwise = iddo F (A) = Sin iT = ot1 F(o)=sin o =0 Since Floo) 1 F is not a distribution function. 3) fra= {cx (6-x 34066 otherwise @ 5 f69dx = 1 ca (6-x) dx = 1

c S6x - x²) dx = cloud - ( [0 1969) - 41216-22) [ 42 - 63] =) c=1/9 (2) F(x) = S fox) dx = 5 + x (6-x) dx = 26 x - x²) de +(924 - (31 -- [3 (2²9) - 7 (x2-27)] =/(x²-9) - 4 Cx²27) 36x26