The likelihood function is L(p)=(710)⋅p7⋅(1−p)3. It represents the probability of observing 7 heads and 3 tails as a function of the unknown parameter p, the probability of heads.
Conditions: The number of tosses n=10.; The observed number of heads k=7.; p is the probability of heads on a single toss.
The likelihood function is L(p)=(710)⋅p7⋅(1−p)3. It represents the probability of observing 7 heads and 3 tails as a function of the unknown parameter p, the probability of heads.
Conditions: The number of tosses n=10.; The observed number of heads k=7.; p is the probability of heads on a single toss.
The likelihood function is not a probability distribution because its integral over the parameter space does not equal 1. It measures how well each parameter value explains the fixed data, rather than assigning probabilities to the parameter values themselves.
Conditions: The data are fixed.; The parameter p is varied over its space [0,1].
The likelihood function is not a probability distribution because its integral over the parameter space does not equal 1. It measures how well each parameter value explains the fixed data, rather than assigning probabilities to the parameter values themselves.
Conditions: The data are fixed.; The parameter p is varied over its space [0,1].
The maximum likelihood estimate is defined as the parameter value that corresponds to the peak (maximum) of the likelihood curve. It is the value of the parameter that gives the highest likelihood for the observed data.
Conditions: A likelihood function L(p) over candidate parameter values is available.; The data are fixed.
The maximum likelihood estimate is defined as the parameter value that corresponds to the peak (maximum) of the likelihood curve. It is the value of the parameter that gives the highest likelihood for the observed data.
Conditions: A likelihood function L(p) over candidate parameter values is available.; The data are fixed.