The shape of a random variable

Set n tries and a chance p, and see the binomial distribution with its expected value and spread.

Interactive

expected value E(X)5

standard deviation1.58

most likely: 524.6%

Number of tries, n10Chance of success each try, p0.5Compare with the bell curve

The math, with your numbers

P(X = k) = \binom{10}{k}\,0.5^{k}\,0.5^{10 - k}

E(X) = np = 5, \qquad \mathrm{Var}(X) = np(1-p) = 2.5

Try this

→n = 10, p = 0.5: what's the chance of exactly 5 heads? Is it more or less than you expected?
→Keep p = 0.1 and raise n from 5 to 60. When does the shape stop being lopsided?
→Which p gives the widest spread for a fixed n?

Want to know why it behaves like this?

The lesson “Random Variables: Expected Value & Spread” explains it step by step: What should you expect from something random?

The shape of a random variable

Set n tries and a chance p, and see the binomial distribution with its expected value and spread.

The shape of a random variable

Interactive

expected value E(X)5

standard deviation1.58

most likely: 524.6%

Number of tries, n10Chance of success each try, p0.5Compare with the bell curve

The math, with your numbers

P(X = k) = \binom{10}{k}\,0.5^{k}\,0.5^{10 - k}

E(X) = np = 5, \qquad \mathrm{Var}(X) = np(1-p) = 2.5

Try this

→n = 10, p = 0.5: what's the chance of exactly 5 heads? Is it more or less than you expected?
→Keep p = 0.1 and raise n from 5 to 60. When does the shape stop being lopsided?
→Which p gives the widest spread for a fixed n?

Want to know why it behaves like this?

The lesson “Random Variables: Expected Value & Spread” explains it step by step: What should you expect from something random?