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14. The number of absences from June to March of a student based on
his class adviser's record is shown below.
Month No. of Absences Month No. of Absences
June
November
2
July
2
December
1
August
1
January
4
September
3
February
1
October
March
If X be the random variable representing the number of absences. Which
table represents the probability distribution?
A.
1
2
3
P(X)
2/10
2/10
3/10
3/10
В.
1
2
3/10
3
3/10
PX)
1/10
3/10
C.
1
3
4
X
P(X)
O
1/10
2
3/10
1/10
3/10
1/5
X
O
1
2
3
PX)
1/5
3/10
3/ 10
1/10
1/10
Suppose X and Y are jointly normal random variables. Briefly discuss bivariate Normal distribution. Your answer should include, but not limited to, the joint pdf of the bivariate normal distribution f(x, y), it's properties including, but not limited to, E(Y/X=x) and V(Y/X=x).
2. A certain radioactive substance has a half-life of 38 hours. Find how long it takes for 90% of
the radioactivity to be dissipated.
1.At 1:00 P.M., a thermometer reading 70°F is taken outside where the air temperature is -10°F. At 1:02 P.M., the reading is 26°F. At 1:05 P.M., the thermometer is taken back indoors, where the air is at 70°F. What is the temperature reading at 1:09 P.M.?
Coefficients linear in two variables
(3x − y + 2) dx + (9x − 3y + 1)dy = 0
Bernoulli’s Equation
(y^4 − 2xy)dx + 3x^2 dy = 0 when y(1)=0
Substitution as suggested by the equation
sinxsinydx + cosxcosydy = 0
Substitution as suggested by the equation
(x + 2y − 1)dx + 3(x + 2y)dy = 0 when y(0) = 2
Integrating factors found by inspection
y(x^2 y^2 − 1)dx + x(x^2 y^2 + 1)dy = 0
Integrating factors found by inspection
y(x^2 + y^2 − 1)dx + x(x^2 + y^2 + 1)dy = 0 when y(1) = 0
