(4 points)\ Suppose you choose at random a number

x

from the interval

5,50

. If

5

, the uniform density function

f(x)

is

f(x)=

,

5

, and

f(x)=0

otherwise.\ Let

E

be the event

6

. In interval notation,\

E=[6,35]

\ What is

P(E)

(write a fraction or use at least four decimal places)?\ Let

F

be the event

22

. In interval notation,\

F=[22,46]

\ What is

P(F)

(write a fraction or use at least four decimal places)?\ What is

P(E\\\\cap F)

(write a fraction or use at least four decimal places)?\ Hint: where do the intervals

E

and

F

overlap?\ What is

P(E\\\\cup uF)

(write a fraction or use at least four decimal places)?\ Hint: Draw the intervals

E

and

F

on a single number line.\ What numbers are covered by at least one of them, and from where to where?\ Note: You can earn partial credit on this problem.

(4 points) Suppose you choose at random a number X from the interval [5,50]. If 5x50, the uniform density function f(x) is f(x)= ,5x50, and f(x)=0 otherwise. Let E be the event 6X35. In interval notation, E=[6,35] What is P(E) (write a fraction or use at least four decimal places)? Let F be the event 22X46. In interval notation, F=[22,46] What is P(F) (write a fraction or use at least four decimal places)? What is P(EF) (write a fraction or use at least four decimal places)? Hint: where do the intervals E and F overlap? What is P(EF) (write a fraction or use at least four decimal places)? Hint: Draw the intervals E and F on a single number line. What numbers are covered by at least one of them, and from where to where? Note: You can earn partial credit on this