The GATE Grind

GATE 2021 MN – Question 59

Engineering Mathematics · Probability and Statistics · 2 marks · Numerical answer

X takes−2, 3, 1 with probabilities 1/3, 1/2, 1/6 respectively. Find E(X²), to one decimal.

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 6.0 to 6.0

Explanation

Square each value of X before weighting it by probability. The three contributions are 4/3, 9/2 and 1/6. Their sum is 6.0, so E(X²)=6.0. This is the second raw moment. Squaring the mean, or taking the variance without adding the squared mean, gives a different quantity.

More Probability and Statistics questions

All Probability and Statistics questions →