Zadanie 7b
Find (i) b; (ii) a,c.
Discrete probability models and means
Construct or use a discrete probability distribution and calculate expected values in context, including fair-game questions.
Tę umiejętność sprawdza 28 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 28 Otwórz w wyszukiwarce z filtrami
Zadanie 7c
Find E(Y).
Zadanie 1a
Find E(M).
Zadanie 1b
Find GM(1).
Zadanie 1c
(i) Find GM′(t). (ii) Hence show that GM′(1) = E(M).
Zadanie 1e
(i) Find p. (ii) Find GY(t).
Zadanie 1f
You may use E(Z) = GZ′(1). Use this derivative identity to find E(Z).
Zadanie 3a
(i) Find a. (ii) State the mode of X.
Zadanie 3b
Find E(X).
Zadanie 7a
Find the possible values of a.
Zadanie 7b
For a=0.1, find Var(3−2X).
Zadanie 1b
(i) Explain why P(X = x) = p(1 − p)x−1 for integer x≥1. (ii) Write E(X) in sigma notation.
Zadanie 1c
For |r|<1, a + ar + ar2 + ⋯ = a/(1 − r). (i) Differentiate both sides with respect to r and express in terms of a,r. (ii) Hence show that E(X)=1/p.
Zadanie 1d
For policy A with p=.12, find E(X) and Var(X).
Zadanie 1g
The distribution of Y is P(Y=1)=1/16,P(Y=2)=m,P(Y=3)=405/1024,P(Y=4)=n. (i) Find m,n. (ii) Show that E(Y)=3019/1024. (iii) Find Var(Y).
Zadanie 3a
Find k.
Zadanie 3b
Find E(X).
Zadanie 2a
Estimate for tomorrow (i) the probability that a kitchen returns at least one container; (ii) the expected number returned per kitchen.
Zadanie 2b
Using the expected total, estimate the minimum number of washing batches needed.
Zadanie 5
A discrete variable X takes values 0,2,5,7 with respective probabilities k,k²,a,k³, where a,k>0. Given E(X)=3.4, find a.
Zadanie 5
A discrete variable X takes values 0,2,5,7 with respective probabilities k,k²,a,k³, where a,k>0. Given E(X)=3.4, find a.
Zadanie 3a
Show that 2k²−k+0.105=0.
Zadanie 3b
Find k and justify your choice.
Zadanie 3c
Hence find E(X).
Zadanie 10a
Show that p=0.40 and q=0.25.
Zadanie 10b
Find P(X>2).
Zadanie 10d
Two independent uniform four-sector spinners each have sector labels 0,2,4,6. Their sum has the following distribution. A replacement pair of independent uniform four-sector spinners must produce this same sum distribution. Their labels are respectively…
- Tabela do uzupełnienia
Zadanie 10e
Two independent uniform four-sector spinners each have sector labels 0,2,4,6. Their sum has the following distribution. A replacement pair of independent uniform four-sector spinners must produce this same sum distribution. Their labels are respectively…
- Tabela do uzupełnienia