Question

Stella Mars Polyte Mo 404 (Probahlty and Statsti Exam (40 poiats) all st D t o The ve distl ta f de i X (2 pts)What is PIX1/2 7 a p) Wht P/2 a/2 iSpts) Whiat is the prohability deasity function of the1audn variable whoe cdf is Fi) T LXbe it zandom vairiable with proability density ftion ot w t What is the valui of C 2tsl What is fhe rumalatjve distnibution of X oI Let X he a toitinnous randon wariable with deniv fuuetion forr>0 otlerwise ehere b> D., What is the aode of X? 3topts For what value of the constaut K, the real value fnction f:-R iven by 1+a-a for random varthle X whige d is a real parazneter is a probability density fus 10pts)Ii the probability of a randon variable X with spece R, (1,2.3. A by 10) is ju)K(2r - . then. fine the value of the constant lk and the cumulative distribution function ofX. t404 (Probability and Statistic) Final Exam (40 points) on Auswer all questions by siiowing all steps to sointion The cumnulative distribution function of a random variabie X is zti Fx(X) 2 1 (2 pts)What is P[X> 1/2]? ii) (3 pts) What is P3/2 X

Answer 1

-15 X<1 Civen F (x)=XtD/2 1 7 d F(X) 1 dx X<- 11 -1 < X 5 1 f)= for -1X) 1 dx PlNoss Plx>2 0.25 2 2-5 Odx =0 i P 3/2 X<5/2=p[1.S< X <2.5 15 pdf for x1 as

Griven, F(x) = -00 X <oo 1 Ite-r のく くω dx 2x dx 2X 2e e Ite to,os) Symmehnic abeut yaxs ラX