{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Practice THREE"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(1) Make a plot of the standard normal curve on the interval [-4, 4]. Give the plot a title \"Standard normal curve\", an x label of \"Normal deviate\" and a y label of \"Density\"."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"image/svg+xml": [
"\n",
"\n"
],
"text/plain": [
"Plot with title “Standard normal curve”"
]
},
"metadata": {
"image/svg+xml": {
"isolated": true
}
},
"output_type": "display_data"
}
],
"source": [
"x <- pretty(-4:4, n=100)\n",
"y <- dnorm(x)\n",
"plot(x, y, type=\"l\", main=\"Standard normal curve\", xlab=\"Normal deviate\", ylab=\"Density\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(2) What is the area under the curve to the right of x=3? In other words, what is the probability of drawing a random number from the normal distribution that is 3 standard deviations or more larger than the mean?"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"0.0013498980316301"
],
"text/latex": [
"0.0013498980316301"
],
"text/markdown": [
"0.0013498980316301"
],
"text/plain": [
"[1] 0.001349898"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 - pnorm(3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(3) If the expression valuse for a gene are normally distributed with mean 10 and standard deviation 2, what is the value of a gene at the 95th percentile?"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"13.2897072539029"
],
"text/latex": [
"13.2897072539029"
],
"text/markdown": [
"13.2897072539029"
],
"text/plain": [
"[1] 13.28971"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"qnorm(0.95, mean=10, sd=2)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Generate 50 numbers from a normal distribtuion with mean=10 and sd=2. Now trnaform this vector so that the numbers have a stnadard normal distribtuion with mean=0 and sd=1."
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"x <- rnorm(50, 10, 2)\n",
"z <- (x - mean(x))/sd(x)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(4) A t-test with 6 degrees of freedom has a score of 3.5. Using only the dt, pt, qt or rt probability functions, what is the p-value if this was a two-sided test? Recall that a p-value is the probailty of seeing a value as extreme or more extreme than the observed score, assuming the score was drawn from the specified distirbution."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"0.0128263383328053"
],
"text/latex": [
"0.0128263383328053"
],
"text/markdown": [
"0.0128263383328053"
],
"text/plain": [
"[1] 0.01282634"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"2*(1 - pt(3.5, df = 6))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(5) Draw 1 million random numbers from the t-distirbution with 6 degrees of freedom. How many times is the numbr less than -3.5 or greater than 3.5? "
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"1310"
],
"text/latex": [
"1310"
],
"text/markdown": [
"1310"
],
"text/plain": [
"[1] 1310"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x <- rt(100000, df=6)\n",
"sum(abs(x) > 3.5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(6) Find the mean value of all numeric variables for the mtcars data, grouping by number of gears and automtatic or manual transmission. (Hint: Use the aggregate function)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/html": [
"