The sum of independent random variables: check 1
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(5,\frac{1}{5})\) variables, with m=3. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{15}\).
Find E(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: review variant 1
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(6,\frac{3}{10})\) variables, with m=4. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{24}\).
Find E(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: check 2
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(6,\frac{3}{10})\) variables, with m=4. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{24}\).
Find Var(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: review variant 2
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(3,\frac{2}{5})\) variables, with m=2. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{6}\).
Find Var(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: check 3
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(3,\frac{2}{5})\) variables, with m=2. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{6}\).
Find P(S=0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: review variant 3
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(4,\frac{1}{2})\) variables, with m=3. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{12}\).
Find P(S=0).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: check 4
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(4,\frac{1}{2})\) variables, with m=3. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{12}\).
Find P(S=1).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The sum of independent random variables: review variant 4
Difficulty: ★★☆Maths4U Original · Short practice
X₁,…,Xₘ are independent \(\operatorname{Bin}(5,\frac{3}{5})\) variables, with m=4. Let S be their sum. Thus \(G_S(t)=(1-p+pt)^{20}\).
Find P(S=1).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.