Remember: If X is a continuous random variable with probability density function f (I), b then P(a S X Remember: If X is a continuous

Remember: If X is a continuous random variable with probability density function f (I), b then P(a S X <_: b f note: unsimplied answers that demonstrate the computation are preferred e.g. as opposed to a: x2 let x be a continuous random variable with probability density function for o s .1: v82 usubstitution integrate show has reasonable by showing total area under curve y="f(LII)" over given xvalues is find p g>

Remember: If X is a continuous random variable with probability density function f (x), then P (a X b) = f (x) d:r. Note: Unsimplified answers that demonstrate the computation are preferred, e.g. (I) as opposed to 21. Let X be a continuous random variable with probability density function f (x) = for O x V"'TZ (use u-substitution to integrate!) (a) Show that X has a reasonable density function by showing that the total area under the curve y = f (x) over the given x-values is 1. (b) Find S X 2).