Question

1. Computational problem #1) Compute all the marginal, joint and conditional probabilities for the following table:

	Achievement of Goal Weight
Weight Loss strategy	Achieved Goal Weight	Did Not Achieve Goal Weight	Total
Diet alone	20	80	100
Diet and Exercise	60	40	100
Total	80	120	200

Answer 1

MARGINAL DISTRIBUTION OF WEIGHT MANAGEMENT BY DIET AND DIET AND EXERCISE

TO CALCULATE MARGINAL DISTRIBUTION PROBABILITY WE WILL LOOK AT THE MARGINS

AND THE MARGIN OF ACHIEVED GOAL WEIGHT = 80

MARGIN OF DIDNT ACHIEVE GOAL WEIGHT = 120  

MARGIN OF DIET ALONE= 100

MARGIN OF EXERCISE =100

TOTAL = 200

ACHIEVED GOAL WEIGHT = 80 / 200 = 0.4 ( MARGINAL DISTRIBUTION PROBABILITY)

DIDNT ACHIEVE GOAL WEIGHT = 120/200 = 0.6 ( MARGINAL DISTRIBUTION PROBABILITY)

WITH DIET ALONE = 100 / 200 = 0.5 ( MARGINAL DISTRIBUTION PROBABILITY)

WITH DIET AND EXERCISE = 100 / 200= 0.5 ( MARGINAL DISTRIBUTION PROBABILITY)

CONDITIONAL PROBABILITY

DIET ALONE= ACHIEVED GOAL WEIGHT / TOTAL WEIGHT

= 20 / 100= 0.5 (CONDITIONAL PROBABILITY )

DIET ALONE= DIDNT ACHIEVE GOAL WEIGHT / TOTAL WEIGHT

= 80/100= 0.8 ( CONDITIONAL PROBABILITY)

DIET AND EXERCISE=  ACHIEVED GOAL WEIGHT / TOTAL WEIGHT

= 60 / 100 = 0.6  (CONDITIONAL PROBABILITY )

DIET AND EXERCISE=DIDNT ACHIEVE GOAL WEIGHT / TOTAL WEIGHT

= 40 / 100 = 0.4  (CONDITIONAL PROBABILITY )

JOINT PROBABILITY

IT IS THE PROBABILITY GIVES THE SAME RESULT BY ADDING TWO DIFFERENT VARIABLES AT TWO DIFFERENT AXIS.

ACHIEVED GOAL WEIGHT + DIDNT ACHIEVE GOAL WEIGHT WITH DIET ALONE

20 + 80 = 100

ACHIEVED GOAL WEIGHT + DIDNT ACHIEVE GOAL WEIGHT WITH DIET ALONE WITH DIET AND EXERCISE

60+40 = 100

TOTAL = 200

LIKEWISE

IF WE WILL JOINT

ACHIEVED GOAL WEIGHT ( DIET + DIET AND EXERCISE)

80 ( 20 + 60 )

DIDN'T ACHIEVED GOAL WEIGHT ( DIET + DIET AND EXERCISE)

120 ( 80+ 40 )

COMBINING TOGETHER

80 + 120 = 200

TOTAL = 200

BY ADDING IN BOTH WAY THE RESULT SHOULD BE SAME , IN THIS CASE THE RESULT IS TOTAL 200