Reasons for Incorrect Statements for the Midterm

Question 1

Answer 1

0, 1, 2, 3, 4

Question 2

Answer 2

0, 1, 2, 3, …, +∞

Question 3

Answer 3

If X is discrete quantitative

Question 4

Answer 4

The equality of the two probabilities hold only if the population mean is equal to 0

Question 5

Answer 5

then P(X=1)+P(X=2)+P(X=3) = 1.0–P(X=0)

Question 6

Answer 6

Question 7

Answer 7

P(X ≥ 1) = 1 – P(X ≤ 1)

Question 8

Answer 8

then 2P(Z ≤ a) – 1 = P( – a ≤ Z ≤ a)

Question 9

Answer 9

then E(X) = np ≠ Var (X)

Question 10

Answer 10

m is the population mean, but X ~ Po(m) is not symmetrical in general

Question 11

Answer 11

then P(X ≥ 1) = 1 – P(X ≤ 1)

Question 12

Answer 12

Question 13

The distribution X ~ Bi(4, 0.5) is symmetrical with respect to 4.

Answer 13

is symmetrical with respect to 4 x 0.5 = 2

Question 14

P(X≤4) = P(X<3)+P(X=4) if X ~ Bi(5, 0.5)

Answer 14

= P(X ≤ 3) + P(X = 4)

Question 15

If X ~ Po(m), then Var(X) = m²

Answer 15

Var(X) = m

Question 16

P(Z = 0) = 0.5 if Z ~ N(0, 1)

Answer 16

P(Z = 0) = 0

Question 17

Answer 17

Question 18

If X ~ Bi(4, p), then
P(X ≤ 2) = P(X ≥ 2) for any p.

Answer 18

Not for any p, only for p = 0.5.

Question 19

If X ~ Po(5), then
P(X > 3) = P(X = 4) + P(X = 5).

Answer 19

then P(X > 3) = P(X = 4) + P(X = 5) + … + P(X = ∞).

Question 20

If Z ~ N(0, 1) and a < 0, b > 0, then P(a≤Z≤b)=2P(Z≤b)–1.

Answer 20

P(a ≤ Z ≤ b) = P(Z ≤ b) – P(Z < a).

Question 21

If X ~ Bi(n, p), then E(X) = np(1– p).

Answer 21

E(X) = np

Question 22

If X is continuous quantitative, then
P(X ≥ 1) = 1 – P(X = 0).

Answer 22

P(X ≥ 1) = 1 – P(X < 1)

Question 23

Answer 23